All we know is what's come out to the public. But there is some evidence of Henry being involved in certain big transactions.
Just a few examples that come to mind:
1) When the Red Sox met with Teixeira and Boras, it was Henry who announced afterward, rather disgustedly, that the Sox were not going to be signing him.
2) He made the statement about it not being a good idea to sign long term deals with pitchers over 30, or words to that effect.
3) Regarding the Sale extension, he said that the team made a mistake in how they handled the Lester negotiations and that they didn't want to do the same thing with Sale.