When you are attempting an analysis of historical records, there is no substitute for looking at the original records.
In her Quicklesson 1: Analysis and Citation, Elizabeth Shown Mills says "Citations are an analytical tool we use to help ourselves reach accurate conclusions." She goes on to explain:
As researchers, we love sources. They provide answers to our burning
questions. But they don’t provide proof. The answers they give us may
be untrue. They may be incomplete. They often contradict each other.
Each time we find a source, we must analyze it to determine what it
is. Then we identify it. That physical analysis and identification of
our source is expressed as a citation. At publication stage, that
citation is typically stripped down to the bare minimum needed to
relocate the source. But, in the research phase, the details we
capture in that citation provide the foundation for evaluating or
analyzing the information that source provides.
As our research expands to include many sources, we find conflicts
between them. Again, the details we have captured about each source
provide a framework for analyzing our body of evidence. In the end,
the proof we offer can be no better than each individual source upon
which our conclusion is based.
So before leaping to the end question of how reliable the FamilySearch extract might be, let's begin with an overview of how that record arrived at your computer screen. A simplified view of the process might look like this:
- People create a law (church or civil) mandating that records should be kept.
- Someone creates that record.
- FamilySearch sends a team to where the record is to take pictures of the record. (Don't forget that records, like people, don't always stay where they were born.)
- Working copies of the microfilm master are made.
- The records are sent to the indexing team, where critical information is extracted.
- Catalog information and citation information are created; the information (along with the extracted data) is published on the FamilySearch website.
- Individual researchers view the records.
What FamilySearch has given you online is a published citation -- as Mills says, "stripped down to the bare minimum needed to relocate the source". To get the information needed in order to do analysis, we need to decipher it as best we can.
Search the FamilySearch Catalog
The FamilySearch catalog allows the user to search by the FHL Film number. Click on the blue link for Film/Fiche to open up the search box:

Then take the FHL film number and put it into the search box, removing the commas. The catalog entry for 1055966 says that it is part of the collection titled Kirchenbuch, 1694-1913; the records were created by Evangelische Kirche Untertürkheim (Stuttgart). The whole collection gathers together "Parish register of baptisms, marriages, burials, confirmations and family registers". Looking at the Film Notes, we can see the notes for film 1055966:
Taufen 1801-1875 Family History Library International Film 1055966
Film notes for your second source are from the line immediately below:
Heiraten 1808-1913 Tote 1830-1884 Family History Library International Film 1055967
Both lines are followed by the icons of a magnifying glass and a film roll.

The first tells us the collection is searchable (which we already knew); clicking on the second takes us to the screen where we can order the microfilm and have it sent to our local Family History Center/Library for extended viewing, if privacy restrictions allow. (The other icon not seen here is a camera, used for collections which can be viewed online.)
The About this record box underneath the film notes has more information, including links to an article explaining the film ordering system, and to a locator that will help you find the nearest Family History Center or library. If you haven't done so already, sign up for a free account, then log in so you can see the available pricing. (Having a free account on FamilySearch is useful even if you don't ever plan to order microfilm -- once you are signed in, you can download search results to your computer in spreadsheet form.)
Before you leave the catalog page, it may be worthwhile to look over the page and see what other records are in this same catalog entry. The next film, number 1055968, has records that might be in your time period of interest, but the records are not indexed -- they only have a microfilm reel icon.
The FamilySearch Research Wiki
For some collections of historical records, the FamilySearch Research Wiki has an article about the individual collection. If there isn't an article specific to the collection, there may be a general one, like this: Germany Church Records. Reading the sections on Baptisms [Taufen] and Marriages [Heiraten] can give you an overview of what else might be in the record that was not included in the extract. The section on Confirmations [Konfirmationen] and Family Registers [Familienbücher] can help you decide whether you want to order film 1055968 so you can browse it and look for your focus family in those records.
Unfortunately, there is no substitute for looking at the original images. You can't tell if the indexers made an error without it. If you are in the US, going to your local FHC, or in the worst-case-scenario, going to Salt Lake City to go to the Family History Library, is easier than going to Germany.
For family history and genealogy, it's important to realize that records are created by people, and people make mistakes. Even if we had the answer to "how reliable" a record set is (which we might get if we find an academic study focused on those records, or can consult someone who has done a one-place study of that individual parish), we would still have to examine the individual records to decide for ourselves if these individual entries were likely to be accurate, or to contain errors. But if you do want to get a feel for how many discrepancies of this kind can be found in records from this time and place, you could search for published case studies from other researchers who have families in this parish or nearby parishes.
The larger question of "how likely is it" that there would be two individuals born on the same day in the same place is treacherous. Watch out for hidden assumptions you may be making when you ask that question. See Document Day: Analyzing Church Records for some of the traps we can construct for ourselves if we take records at face value. It is a good example of why Elizabeth Shown Mills reminds us:
- There is no such thing as The Gospel According to the Church Clerk.
- Identity decisions based on “the name’s the same” or “the only one” often come back to bite us.
- We can’t do reliable research by consulting just one kind of record....
In their attempts to make genealogy and family history easier for us, all of the genealogy websites also make it harder, because they over-emphasize searching for and matching records by name, and they obscure the nature of the original records.
Further Reading and other resources: