Based on what I've read on this, I can see why Trump and Elon MIGHT feel like the return flight was held back for political reasons... But I'm not really able to take either side of this argument as it stands, so I'll give my thoughts for why that is in the hope someone might be able to convince me one way or the other...
Firstly, the assumption that NASA is apolitical should be questioned. This might just be my ignorance, but I still haven't seen any good reasoning for why NASA would delay the return flight. As others have noted the capsule was already there, but NASA seemingly just decided to randomly keep them up there months longer than necessary? Why?
And while it's not fair to blame the Biden administration for this directly, ultimately the actions of any government agency would be the responsibility of the current administration to some extent, so if there was any suspicion that the return flight was being pushed back for political reasons the Biden administration should have intervened.
I imagine if Elon did push for an earlier return and was denied this without a good reason he might have questioned why, and I could imagine someone in that position might assume a political motive – perhaps reasonably depending on those private conversations had.
I also think there's an argument to be made that if the Biden administration was friendlier with Elon and didn't go out of their way to alienate him that this return flight would have happened earlier too. Perhaps because Elon could have spoke to Biden directly as he did with Trump, or because NASA would have changed their calculation on the PR of the return.
I have tried repeatedly to find a reason why the return flight might have been delayed, but haven't been able to find any good reason for this so I'm on the fence about why this might have happened. If someone can give me a reasonable explanation for why they weren't returned earlier (especially if it's a reason Elon would have been aware of) I'd likely conclude Elon is most likely lying.
Either way the argument, "Elon is wrong because the capsule was up there the whole time so they could have been brought back whenever, but NASA just decided to push it back" is not a convincing explanation that there was no political calculation here.