If used in the case they were likely authenticated via certification or sworn testimony, used in the trial and returned to the parties. Otherwise court files would have all kinds of evidence stuffed in them.
I see no decision in this case relating to the location of birth of Obama Jr, which could require either party to "prove up" their statements with evidence. It would however be good legal practice for one or both attorneys to have at the ready any evidence they may want to present to prove or disprove any subject matter of the trial especially if it was contested.
A court file is a summary of filings, motions, findings and appeals. It may make reference to documents or transcripts or other evidence, but they generally are not in a file.(attorneys usually keep everything, used in court or not to cover themselve from malpractice claims)A record is made of the trial usually by a court reporter (small claims tape recorder) an is not printed out as a transcript unless one or both parties request it (usually for appeal)and pays for the transcript.
Things I have seen and am aware of being sealed in civil cases could be medical records and statements of income by those claiming inability to pay costs. These items are usually in the file in a separate envelope on top marked CONFIDENTIAL which the clerk handling the file would not copy or would remove prior to allowing inspection of the file. While the pages marked show 12 pages and only 7 are shown, it does not mean the others are sealed. I believe in this case an investigator went directly to the court, and had the documents they chose as relevant copied, and did not have the others copied.(frugal) If the other pages were sealed any experienced investigator would have made note of it and posted it with the copies. If there was something sealed in the file other than the two reasons I cited above, it would be a lead to get it unsealed in one of the current cases or that information of value could be in the sealed envelope. JMHO.
My divorce records are on file in the county I was divorced in. I had to submit birth certificates as evidence to the proof of the birth of the children (I guess so someone doesn’t get a court order on kids that were from a previous marraige or just made up. hey, I’ve seen screwier). However if you were to go and get a copy of the divorce records, it would only the be the petition and final decree. If you went to my lawyer’s office, you would probably find the documents submitted as evidence though.