You can't know that a particular record at Family Search (or any other vendor) belongs to your ancestor by analyzing the information in that single record and doing nothing else. Records that were made in 1845 or 1846 are so long ago that no one alive could know. All you can say is that elements of the record are consistent with other records that you believe to be your ancestors.
The Ancestry Insider talked about the nature of genealogy in several posts, two of which were titled The Chasm. In the post from Mar 21, 2011, he outlined three stages of genealogical research. I'll add a bit to his definitions from my own experience, but we are basically in agreement.
- We fill our pedigree and family group sheets with information we know, about people who were known to us personally, and (if we are not the oldest generation in our family) people who were known to our older living relatives. Your own knowledge is personal knowledge. Your relatives' knowledge is their own personal knowledge, but to you it is secondary -- "Uncle John says so".
- We extend our knowledge through vital records (and a few other types of records) which hold in a single record what seems to be a complete picture of an individual in a family context. This is secondary knowledge, someone says so.
- As we push beyond the era of vital records, no one record describes a complete person, and we are forced to cobble together a picture of them with fragments that we gather from other records.
The gap between what we know from living memory and from direct evidence, and from the history we can only know from records, and from combinations of records, is what the The Ancestry Insider calls The Chasm.
He returned to this idea in a post dated April 22, 2013
On one side of the chasm are the ancestors and relatives we know
personally. We know them as people. We grew up with them or with our
parents talking about them. On the other side are ancestors and
relatives that we know only through records.
On one side of the chasm we utilized living memory—our own and our
loved ones.’ On the other side we utilized records.
On one side of the chasm are the modern census and vital records that
uniquely identify individuals and relationships. On the other side
records are incomplete, spotty, illegible, unindexed, hard-to-locate,
or offline. Records are indispensably helpful, though seldomly so.
On one side of the chasm we blithely used direct evidence. On the
other side, we painstakingly categorize, compare, contrast, correlate,
and cite direct, indirect, contradictory, and negative evidence.
Genealogy big-box vendors, especially those who encourage hint-driven genealogy, cater to people who are in stages one and two, who are looking for records which contain direct evidence that answers the question they want to know.
When these new style online-only genealogists they get to stage three, where inferential genealogy is necessary, they are bewildered and don't know what to do. They have been trained by the big vendors to collect vital records and census records and match them up by name, and they don't know anything else.
F. Warren Bittner, CG, in his webinar Complex Evidence: What it is, How it Works, Why it Matters called the collecting of birth, marriage, and death records False Research Imperatives. Too many times we collect birth, marriage, and death records for our ancestors, then we think we are done. Meanwhile, we ignore all the other information that might be available that would give us a more complete picture of our ancestors.
As GeneJ said -- we've all been guilty of premature connectivitis syndrome. But you will be on much better ground if you use the elements of the Genealogical Proof Standard, and do more than simply picking out the records that happen to match by name, and then thinking about those records out of their historical context.
When a genealogy vendor cherry-picks the records that seem to match an ancestor by name, they lead us to make the conclusion that these are our ancestors, ahead of examining other evidence, and instead of looking at other research paths. We start looking for reasons to back this conclusion up. We don't always stop to learn about the records themselves, to think about who created them, or for what purpose. We ignore basic fundamental questions about the surrounding communities that could be asked first.
What do we know about the area from which these records come? How much coverage does FamilySearch have? We assume that any records that were made about our relatives survived and there was no record loss. Assuming that a particular group of records must have records about our ancestors in it is never a safe assumption to make, especially when doing research in Germany.
You said: "(I am not sure if the family as a whole emigrated or if only Mélanie emigrated when she became adult, but this is not my question anyway)". But this is precisely the question that you need to consider before you leap back to Germany. Finding out more about how your ancestor emigrated -- establishing her as a member of a group -- can show you the way back to the correct part of Germany.