I don't think it stretches anything. The opposite -- that different websites, with interfaces that all vary subtly in a billion different ways, with different traffic sources, with different market positions, with different primary outcome goals -- are able to be compared? I would need to see quite a bit of specific evidence to believe that.
I've worked with brilliant conversion optimizers, in a single vertical niche where we had > 30 websites, each doing between 200K-2M visits/month. We would have loved to test + copy, but every time we ran this experiment, we found huge differences.
One subtle nuance is that "generalizable" needs to be more specific than "this change increased conversions". The true goal of optimization is not the find the B that beats A; it's to find the global optimum.
The Conversion industry tends to similar language as the complementary/alternative medicine space. "I did this thing, it had this outcome. I believe this happened because XYZ. It worked for me, it will work for you!" (People telling stories which may or may not be true.)
That is also why clinical trials for interventions is so important.