In my opinion, Beck with an ATW instead of TATW is not HHJATW - ATW. HJATW is one movement just like HTATW where as the 'Half Beck' trick is clearly 2 movements. For me, it should in fact be called hatw aatw nt. I agree with Dan that this sort of debate is fairly useless. However, when it comes to a competition like the sick 3 in Prague, it causes a lot of controversy as to whether a combo is 3, 4 or even 5 tricks long.
Moving onto the K3EATW/SZATW discussion, I agree with Max. I feel very strongly that the majority of people who do SZATW, don't do it the way it should be done. When Szymo first did the trick, I saw it as an LTATW just without the touch of the crossover. Where as, now it is done only with 1 jump which I personally don't think is right.
I hate to single people out specifically but here are 2 examples:
For me unclean by Japa -
Japa - SzatwReal, clean SZATW by Mumin -
Mumin - Szymo atwJust my opinion but I think I'm right with what I've said.