Not to put too fine a point on it but if there are blind trials showing no effect and non-blind trials showing an effect, my conclusion would be the effect is a placebo.
I've tried different L-Theanine supplements, and there's definitely a difference in quality across companies... which could help explain the variance in experiences.
Unfortunately, there isn't much regulation for supplements in general. Some companies do 3rd party purity testing, though it's not always the case.
That's a reasonable take but still depends on the trials. E.G. if the blind trial was 20 college age Americans males, and the non-blind trial was 1000 people from various ages and countries, I'd probably lean towards trusting the non-blind trials (unless I happened to be a college age American male).
Or if all the available trials are n<=20, I'll probably lean towards trusting the anecdotes, at least enough to try the supplement for myself.
When it comes to cheap-to-produce supplements, very limited trial data is the norm, unfortunately. There's no money for running large trials.