Yeah, you are right. No search engine will help if people refuse to provide the correct data. Instead of lying (by omission) in person we get lying (by omission) in search engine results.

There could be an option to verify or provide the option externally. For example after meeting a person, you could open their profile and write what you think are their traits (not all of them, only some of them that are wrong or missing). If many people correct or add something, it could be displayed in the person's profile. -- But this would be rather easy to abuse. If for whatever reason I dislike a person, I could add an incorrect but repulsive information to their profile, and ask my friends (with some explanation) to report that they dated the person too, and to confirm my information. On the other hand, I could ask my friends (or make sockpuppet accounts) to report that they dated me, and to confirm a wrong positive information about me.

Another option could be real-life verification / costly signalling. If a person visits the dating agency personally, and shows them a university diploma / a tax report / takes an IQ test there, the agency would confirm them as educated / rich / smart. This would be difficult and costly, so only a few people would participate. Even if some people would be willing to pay the costs to find the right person, the low number of users would reduce the network effect. Maybe this verification could be just an extra service on a standard dating site.