Nah, it's a self-defense strategy: it's about protecting them and their views, careers & "treatment" market. From the very beginning there was posing as victims and prominent indignance at supposedly not taking the disableist imput of psychiatry seriously, which was presented like it was at the detriment of those poor, poor patients they were just trying to help (while stigmatising them at the same time).
It's indeed good to look at what's missing if this was a good faith letter. Not just objective proof of unjust criticism, but also concrete and practical proof that Long COVID's "bodily symptoms are caused or worsened by psychological factors" and how precisely "There is no chance of decent care for this heterogeneous group of patients if psychosocial factors are not taken seriously when considering differential diagnoses, clinical formulation, and appropriately individualised management plans."
I don't mean the usual talking points, I mean actually showing that there is "no chance for decent care" for viral persistence, infection-triggered autoimmunity, latent virus reactivation, inflammatory cell damage, organ damage, blood clotting and all the other concrete pathology unless you involve talking about your mum, explaining how Long COVID on television makes you think you have it, and telling patients to go to bed on time.