The Supreme court did find evidence for the Ram temple from various accounts. There is no single point Hindu organization that could claim ownership to the property and hence used the adverse possession clause for right to ownership.
Coming to the judgment, I'm pretty sure those 5 judges with years of experience doing what they do (non sanghi) best trump those non sanghi experts. This whole issue has been made into an emotional mumbo jumbo with the destruction of the mosque, which could've been solved amicably. Regardless the verdict still would be same.
The Supreme Court, in its judgement, relied on the ASI report, and made the following observations. I have included some of them here for your benefit (there are other observations as well, but I included only a few to make my point)
1. The possible linkages of Buddhist or Jain traditions cannot be excluded
2. Though the excavation has revealed the existence of a circular shrine, conceivably a Shiva shrine dating back to the seventh to ninth century A.D, the underlying structure belongs to twelfth century A.D. The circular shrine and the underlying structure with pillar bases belong to two different time periods between three to five centuries apart;
3.
There is no specific finding that the underlying structure was a temple dedicated to Lord Ram; and
4. Significantly, the ASI has not specifically opined on whether a temple was demolished for the construction of the disputed structure though it has emerged from the report that the disputed structure was constructed on the site of and utilised the foundation and material of the underlying structure. found evidence of a temple, there was no judgement of its origins, faith or ownership.
I hope this offers a better understanding to the situation.
If the judgement only addressed the title of the land (which was the original issue), then the Muslim party would win this, since they held the documents showing ownership of the land. Amusingly, the Indian justice system decided to make an idol based on a mythical figure a party to the dispute. Think of it in terms of Mickey Mouse laying ownership to Disneyland.
India's justice system has been compromised. All institutions in India are being systematically weakened. There is no doubt about this. Look at the recent judgments on any of the issues. Habeas Corpus petitions are being ignored among other things.