That's one of the questions Sony should clarify. Did they just test the games if they were bootable or if they were completely playable start to finish with no bugs. Ubisoft's list suggest that Sony just tested if games were bootable and Ubisoft personally found out the games were not playable.
I very much doubt they tested all games all the way through for all bugs. That's not remotely feasible.
My guess is they test them for a set period of gameplay, not the entire game. To test over 4000 games to completion (including side quests etc) is an unfathomable task.
Say those 4000 games have an average play time including side content of 25 hours, that's over 100,000 hours of game testing time, or around 12,500 days of 8 hour work day testing.
Even if you had a team of 10 people testing said games for 8 hours a day, it would take them well over 3 and a half years to test them all, since that's not taking into account data recording, notes, annotation, side work, breaks, procrastination etc.
BC will never be completely bug or problem free. You only have to Google Xbox One backwards compatibility problems to bring up a long list of people complaining about BC bugs on that system too. That's ignoring that even non BC games can have bugs. Hell, Syndicate is buggy even on the PS4 lol.