The countersinking is actually easy. Just use a drill bit to open up the current hole a bit larger. You only need to drill in the depth of the piece that sticks in there; don't go all the way through.

COuld you just get longer screws?

Or am I not getting it?

It's not the screws that are the issue, it's where the screw goes into the pulls. It sticks out significantly and is meant to go in the hole on the drawer. I'm not explaining this well but you can see it on the right hand side of the picture. I have my sample one on my drawer now and there's a huge gap and you can see the cylinder part where the screw goes in.

I guess if I decide that I want them, I'll just drill a larger hole. I was just hoping there was a pull out there that wouldn't require making a large hole in case I want to change them in the future.

Just checked Hafele catalog- only one of the bin pulls they offer needs to be countersunk, the other dozen or so don't (many are contemporary though).
I'm certain that the majority of bin pulls don't require countersink so you should find one that suits from some mfg. somewhere.
The Hafele you want to avoid it # 151.08.708

Does this same pull come with 3 1/2" centers?