That's my thought as well, what is there to gain by making a claim like that in private if it's entirely false? To blow off steam? Especially considering he wasn't even close to coming out of retirement at the time, so it's not like he been on the Rams coaching staff and had a dog in the fight.
Not true, he was projected a 4th-5th rounder on the NFL's own page and pre-Combine/before he came out, was projected to go as high as in the 3rd round according to CBS. The NFL even sent a camera crew to his house (something they only did for players drafted in the first 4 rounds) because they were anticipating him getting drafted. When he began to fall hard, the league couldn't have him go undrafted as they proceeded to show a live look-in to his living room every time a DE not named Michael Sam was drafted and simultaneously look like a bunch of bigots causing them to miss out on the revenue from the LGBT-community potentially looking to buy his jersey. The NFL says money is money.
Concur, the NFL has proven time again that they will discredit or outright suppress any information they feel will affect their bottom-line. If they feel a particular situation has the potential to harm that revenue stream, they'll get out in front of it if they can and do the damage control they can. Contrarily, if they're confident it won't get out, they'll suppress it entirely.
The Ray Rice elevator video is a prime example of both aspects of that; they had the video in the league office and still only gave him a 2-game suspension because: a.) they were confident it wouldn't get leaked since they had it in their possession so they issued a "harsh" sentence and released a statement about a "zero tolerance policy" regarding domestic abuse-blah-blah-blah, and b.) having Rice on the field for 14-games and potentially winning "Comeback Player of the Year" after an injury-riddled 2013 season was a win-win for all parties involved. Then TMZ still got their hands on it, it blew up in their faces and sent the league scrambling to put out the fires.
There even being a shred of credible evidence to that claim is part of the reason I think they're refusing to release all the email evidence they have. If any information of the league incentivizing/outright forcing the Rams to use a draft pick to select Sam gets out, it will permanently tarnish the league's relationship with the LGBT-community and all the "goodwill" earned from ousting "that bigot" Gruden will dissipate and generate far more controversy for the league than anything Gruden ever said.
Keep in mind, at this same time Kroenke was in the midst of an ongoing battle in attempts to move the team out of St. Louis and to Los Angeles, which only ~8 months later he announces he's teaming up with a capital group to build a 70,000-seat stadium in Inglewood and another year later was approved to relocate. Potentially a bit of a "you scratch my back, I'll scratch yours" between the league and Kroenke.