I think one question you want to ask yourself is why you want to fix it. I have a fade myself, but I want to fix it not because I think a draw is better (I don't, I think a fade can be a better ball and more reliable than a draw), but because the way I'm hitting the ball I am not coming from the inside enough, and I'm coming over the top on my downswing. I have too many compensations that worked for a while, that aren't working now, and that need to be addressed, and I'm trying to address them as well as I can.
Falling back may contribute to an improper impact position (weight isn't forward enough), but it may not the real reason you're slicing. I imagine that thinking you have an object under your foot (ball, sponge, etc), helps to brace your right leg in your back swing so you don't sway (re: steady head). I've been personally playing with that idea by pushing my right knee in about an inch before I took my club head back. I then felt as if I was stacked with all of my weight being centered over my instep, rather than my weight falling to the outside of my foot (still a work in progress). It may or may not work for you, talk to your pro about it.
It may be a permanent solution if your swing path/club head position at impact/alignment are all promoting a draw, and falling back was the only reason that your club head would have been diverted of it's original track (I would think that a slightly open face at impact, but the club head diverting at impact to the left instead of keeping it's course. If someone better at biomechanics could contemplate this, maybe I'm dead wrong :) ).
I think my point is that even though your swing thought has given you better results, it may not be the primary culprits of your fade/slice. It's something that an instructor/Trackman/video analysis can really pinpoint better than most (get it, GET IT???? I know, I'm an idiot).
Hope this helps, and have fun.
p.s. I hope the "guy" who told you this isn't some "guy", but rather a PGA Professional whom you trust. Be careful of unsolicited advice, it could potentially hurt more than help (speaking from experience, I blew up a potential round in the low 80's at a legit course by listening to some dude I got paired with, and subsequently shooting 10 over what I would've if I hadn't paid him any notice).