It is true for at least one side of the cabinet. If you either undersize the pullout (i.e., a 15" deep drawer instead of a 24" deep one) or just keep the plumbing to one side, the other side can pull out without a problem.

We put a 3" inner "channel" in the island to make room for the full pullout.

With an island loop vent, you don't have room for anything else. That either goes in a pony wall, or fills up your cabinet. This is code acceptable everywhere. Not all jurisdictions accept a Studor vent, as they are less reliable and need changing periodically.

They told you the best workaround. Build a wall. Either that or cut your drawers.

Thank you all. Great ideas. The easiest option seems to be to cut the drawers. A standard trash can isn't 24'' deep, so I don't really need the full depth. Does it mean I need to cut drawer glides, so instead of 24'' they are 15'' or whatever? How much depth does plumbing typically need, is 12'' OK?

It's the drawer sides not depth that you need to change. Take a look at picture of our IKEA island trash pullout thread above. My plumbing comes out of the floor.

I agree with beachem.