The arguments that Melvin lied about closing their position are as follows:
1. Short interest on GME is still high, even after they claimed to have closed their short position.
2. They have a "huge incentive" to lie about this, because people believe it would encourage a selloff.
That is the entirety of the evidence. It is uncritical despite the fact that it gets frenetically repeated on reddit. Here is the evidence which suggests they didn't lie:
1. That first argument doesn't prove what people believe it does. First, short interest is only officially reported twice monthly, and most cited data is out of date or estimated. More importantly, short interest is an aggregate measure which does not track specific positions. It only tracks all positions together. Other firms which haven't been burned by the price increase have opened new positions, hoping to short from the top tick (or thereabouts).
2. The second argument is reddit cargo culting "game theory", and it violates both logic and Occam's Razor. If you're a fund manager who lies to the public about closing a highly volatile position that could bankrupt you, you are facing securities fraud and violation of fiduciary duty, respectively. Either of those will pierce the veil of your firm and leave your personal assets liable for reclamation by the SEC and/or angry investors. You will be sued. You will lose.
Moreover, the "incentive" of this move is that you might prompt a selloff and get to keep your short position. It strains credulity to think someone would make such an uncertain bet with a huge psychological component when their firm is literally on the line. If you're wrong, your firm is dead and all of your personal assets are up for seizure in the ensuing fallout for the aforementioned reasons.
The alternative is that you just close the position, don't lie about it, and your firm survives and you just have a bad year. You are personally unscathed as the fund manager. And since you've had historically excellent returns and this was a 3 or 4 sigma event, long term you'll probably be fine. You'll have a new signal to incorporate into your portfolio risk management and you'll move on.