NOt at all true. Just don't hang a big pot over the edge. The pot needs to fit the eye.

It's not true.

What possible reason did they have for not doing induction on quartz?

As a counter material, 'quartz' should be fine. As a back-splash material over a range or gas cooktop, then threads (discussions) in this forum related to quartz back-splashes should be consulted. Pulling a red hot pan off of an induction hob and setting it directly on the quartz counter instead of onto a trivet or hot pad will prove to have been a bad idea, just as it would be if pulled off a gas burner.