Guys, thanks so much for chiming in (while I was sleeping it off here on the old continent)!
Some of you might have slightly misunderstood the issue, which is probably due to my somewhat unclear description. I guess "involuntary hammer-ons" comes closest and makes more sense than "involuntary tapping", as the problem comes from the fretting hand.
Still, most of you confirmed my suspicion that it is "bad" technique so far (and often related to timing and sync'ing) that I will need to rectify by deliberate practice!
I indeed don't want to "mask" it, and also I prefer rounds to flats
There were a number of interesting novel aspects about the subtleties of fretting in your replies as well - thanks for that!
As for the action on that bass (by the way, it's a Fender Geddy Lee Jazz (MiM) and not a Rick; I think another poster had a Rick as an example): I am only the second owner of this bass, and the first hardly played it, but it seems the nut groove of the E string was/is too low directly out of the factory!?! Which means, until I fix this, I can't get the action lower (on the E string). Besides, that stupid access (non-access) to the truss rod on a Jazz is making it no fun to do adjustments... (But, I also have similar issues (clanking) on other basses with similar or lower action).
Anyway, thanks so much again - lots of input to work further with!