I've never seen any hard numbers on it.
It does only stand to reason that you have a higher chance of escalating an injury if you only have 4 days of rest vs. 7.
Then again, the flipside is you have 10 days to rest after your TNF games vs. everyone else with only 7.
In addition, the Thanksgiving games have been on for forever, and no one has complained about those. At most only a couple teams will have two Thursday games, and if they do it's because of Thanksgiving.
Then again again, I wouldn't listen to any rumors about TV networks - they are just trying to get the NFL to sell the next TNF package for less. The dark secret is NFL packages are barely profitable, and that's before the ratings drops we've seen over the last couple years. Networks jumped to get them not because they make profit but because it is the best way to promote new TV shows ("Watch Young Sheldon!"), it's the best way to sell luxury ads to business assholes that don't watch TV otherwise (next time you watch a game, notice how many Acura and Tag Heuer ads there are) and every time they have the Super Bowl they win the overall ratings numbers for the year (the TV business is so fragmented that yes, the Super Bowl wins, and the AFC Championship shifted CBS a spot up a couple years) and can use that on advertisers when they set ad rates.