I think this is where they got confused:
There's a rule that says if you jump over an
illegal object ball,
and that ball moves, then it's always a foul. Doesn't matter if that ball moved
due to the cue ball, the stick, your sleeve, your hand, etc.
Any movement is a foul.
I think they made that rule because people will often skim the blocking ball
with their cue ball, and then try to say "no, it was actually my stick that moved it.
So it's not a foul." This leads to arguments because it happens so fast it's hard to say for sure.
So the rule was changed to basically say: "if it moves, it's a foul, period".
But again, this only applies to illegal object balls.
I think your opponents missed the word "illegal".
Here's a cut and paste from the BCAPL rulebook on their website:
2. If you attempt to jump over or massé around an impeding illegal object ball then Rule
1-33, Disturbed Balls, does not apply to the impeding ball for that shot. If the impeding
illegal object ball moves during the stroke it is a foul regardless of whether it was moved
by your equipment or any part of your body.