your absolutely right (but not totally)

muscles cannot push.
muscle fiber can contract only, but...
they can pull in opposition to other muscles that in tention, enlongate (i.e. the tounge.)
And... yes, abs are in front and underneath when on a bike but they do still preform balance, stabilization and help with support.
The back muscles do take a higher load, but they are smaller muscles that depend on (here we are) the ABS.

So no, there is no santa claus, muscles only pull, and working your abs does make ayou a better cyclist.