That’s true, but not for the reasons people may think.
The damage was likely due to too low an octane rating, not lack of lead.
When lead was added to gasoline, achieving the octane rating posted on the pump was easy. In fact, the gasoline being dispensed often had a higher octane, sometimes 1 or 2 points higher. So an “87” octane gasoline was really “88” or even “89”.
When lead was banned it became more difficult for refineries to meet, much less exceed, the posted octane. So what was once “88” or “89” is now exactly “87”, or even “86.9”.
The result was cars that formerly ran fine on “87” (which was really “89”) were now experiencing light detonation (“pinging”) far more frequently. Which can cause valve damage and valve-seat recession.
The UND experiment with unleaded avgas bears this out. First off, they didn’t use 100-octane unleaded avgas. They were using Swift’s 94UL with six points less octane. The engines they used are relatively high-compression (8.5:1) with advanced ignition timing of 25-degrees, both typical indicators of the need for higher octane. Originally certified for 91/96 avgas, they now show 100LL on their type certificate. In effect, they were being run right at the limits on 94-octane and some engines didn’t make it.
(as an aside - the Continental C-85, C-90, and O-200 engines like those found in Cessna 150s, Piper Cubs, etc. have a compression ratio of only 7:1. Their octane requirements are minimal. Those engines have been happily burning unleaded mogas for decades. Yet no one talks about a wave of valve-seat recession in those engines).