If I remember and understand correctly, IC had only done a PCR test, and even than did not follow the original study's PCR test
Yep. Theoretically, PCR is a very powerful tool. But lots of people -- even scientists, sometimes -- seem to think that if something is very sensitive and very specific for analyzing a sample, that that's the end of the story. It's not. You have to make sure that your samples are a good representation, for one -- if the thing you're looking for hides out in a tissue you didn't collect, then you're not going to find it with even the best PCR assay. Just as a single example. There are plenty of other potential problems that make it a lot more tricky than providing a simple yes or no, particularly when the questions around this virus are things we don't fully even know how to ask correctly yet.
Culture has some problems, too, as does everything, but WPI tested in multiple ways -- PCR, culture, even sequencing of some samples. That gives me a pretty high level of confidence in their work -- they found something, at least sometimes, across multiple different methods and across three different labs. They may have missed some positives, they may have gotten some false ones, but overall they got enough solid result with enough practical confidence-building measures to say that they definitely found something noteworthy in the samples they had. If their work is really wrong, it's probably not going to be because their tests were all invalid.
The IC study, by contrast, used one testing method, which was different from any at WPI, that they really didn't validate well beyond "can pick up the virus in a sample that looks very little like an actual sample", got totally different numbers, didn't bother to go back and make sure that wasn't their testing method or handling technique, and then came out with very strongly worded statements (this is the part that is inexcusable to me, as a scientist. It's fine to run with the study you have, and it's fine to take your data at face value, those are good things -- but to come out with this study and act as though it's all solid and clear is crap. There's coming across as confident, and then there's coming across as arrogant. These folks managed the latter.)
Really, Wessely's involvement is neither here nor there to me as far as the science goes, but it's also fair to say that if they wanted people already involved in this stuff to trust their study, they'd have been better off without him touching any of it. Especially if they weren't going to go some extra mile to dot their t's and cross their i's as far as methods go.
I don't think we should entirely dismiss their results. I think we should be critical of both studies, and willing to accept that either set of data may be the stronger reflection of reality in the end. But I also think that the WPI study is far, far superior in terms of thoughtful design and careful confirmation of results. It's going to take a lot more than this single, rather problematic UK study to knock it down, in my mind.