Of course it's possible to be excessively aggressive on social media, and it is possible to over-interpret most things on social media as well. The CBT/GET folks are losing their grip on the situation and are scrambling to do whatever they can to hold on to their domain. Of course they'll jump on offensive tweets or whatever, but they will jump on inoffensive ones as well and continue making their bogus arguments no matter what any patients tweet.
There have been many tough but cogent responses to the recent BMJ blogs, Garner's included. For the most part, the responses have seemed entirely appropriate. While the CBT/GET folks will rally round each other, I assume there are also neutral observers reading these cogent responses. To focus on some off-color tweets as the problem or as anything other than some off-color tweets seems off-point to me.
Of course Garner was writing personal posts. And of course his role as a key evidence-based decision-maker writing his personal posts in a high-profile venue for clinicians endowed his posts with more perceived authority than patients writing what they think in social media. In his last post, he blurred that line in a way that smart editors should have prevented. Since they didn't, it seems entirely appropriate to call him out. If that further induces him to make unwarranted claims, it is not inappropriate to counter those as well. Whether it matters in the end is another question. But patients are not at fault here in responding in strong terms.