I think there may be two different arguments that may get conflated.
The important one for me is this.
Because people recruited for PACE knew they might have to do GET the cohort cannot be taken as representative because people who knew that exercise made them worse (or had heard so) would be likely not to have volunteered. The risk/benefit analysis for GET would then be skewed to inappropriately positive. This means that the results cannot be extrapolated even to an Oxford defined population. Using Oxford would have been valid to a first approximation if applied to patients fitting Oxford if there was no recruitment bias of this sort but since it is more likely than not that there was bias then the problem with the recruitment is not the criteria used but the built in bias.
The more philosophical argument is that the BPS people appear to be setting up a trial that will not recruit people who fit the theoretical justification for CBT they claim to be basing their approach on. If the claim is that you need CBT with its mysterious 'cognitive strategies' to deal with a phobic fear of exercise then that's OK. But nobody actually thinks this is a phobia in that sense, I suspect. moreover, the rationale draws on stuff by Richard Edwards that says that when unfit people exercise they do actually feel awful. But the more one looks the more it is clear that none of this was really thought through.