I don't believe it's a myth at all - I'm speaking from considerable experience. I have tried a large number of SET amps over the years with Tannoys (and many dozens of amps altogether, owned, borrowed or just visiting), from fleapower 45s and 2A3 (with Tannoy Monitor Golds) right up to 845s, 211s and even 60w Kronzillas with T1610 with Monitor HPDs.
I owned Silvercore 833C monoblocks with the 833A transmitter tube for a while and thanks to the nice stuff they were doing higher up, almost convinced myself they were up to the job in the bass as well, but against my current Leben, the gap in bass performance was clear, and I eventually had to admit it.
In general with Tannoys and SET (to a greater or lesser extent depending on the particular speaker and amp), while the perception may well be of 'strong' or prominent bass, compared to a more suitable amp there is always lack of bass control, expressed either as lack of definition, or lack of extension, or indeed as both. This may not bother some people (and I've heard people deny the problem even while I've been sat listening to it myself) but it certainly bothers me.
I have tried a couple of OTL amps (not including Atmaspheres, it has to be said - they are fairly uncommon here in the UK) and essentially found the same issues as with SET. Though I'd be the first to admit it's not an amplifier topology I've had much experience with, compared to tube SET/PP and assorted solid state.
If you know of an Atmasphere amp in the UK I could have a play with I'd be delighted to give it a try,