So for me, its much more complex:
1. If you send Lamar out there, it'll be obvious he's hurt. Defense sees that and knows he's not a threat to run, and arguably, isn't a threat to pass. At that point, stopping Henry isn't really super difficult with a loaded box. He got stopped short of three yards multiple times in that game.
2. If you don't send Lamar out there, everybody in the world knows Rush isn't throwing. So again, telegraphing.
Basically, if Lamar is limping out there and unable to run, I think punting provides a much, much greater win probability than having both sides knowing you're running on 4th and 3.