Of course they have a horse in this race, they're literally in the middle of it and Qatar is looking for a way out of it's own sanctioning mess. So honestly it's not surprising that they aren't regurgitating propaganda, it would not make sense to do so, even if Qatar has questionable links with Iranian interests.
Indeed there's space for misdirection if Qatar is more friendly than is suspected, but that's suspicion for the sake of it, it still matters somewhat.
Now, one could say that a timid associate nation counteracting Iranian propaganda might make a few more Iranians sceptical (I imagine a significant minority or even majority already are and have just normalised it), it won't mean anything unless it actually drives momentum against the Clergy and the Revolutionary Guard.