I'm not sure this is true. Many of the bit twiddling hacks can be used in NEON and they have a few unusual instructions I'm dying to play with.
I'm not sure which bit hack you're talking about that's done with a multiply or multiply-add. There's a nice use involving De Bruijin sequences for doing lg2 of a single bit that's very instructive - is that what you meant?
Also multiply adds can be fused so if you're doing that it cab be faster to just multiply by a different number instead of bit twiddling.