Curious situation.
I recently bought an unknown model Bianchi. Its a mix of parts and I can only assume the cranks (marked Bianchi) are original. The PO "thought" the original wheels were a set he threw in that had Shimano Golden Arrow hubs with Ambrosio rims. I have to rebuild the rear hub on this set as the axle was snapped. The set mounted when I purchased the bike were Ofmega hubs with F.i.R. rims.

The issue is the brakes. They are Shimano BR-5500. These are standard reach 43-57mm. As far as I know the BR-5500 should fit any 700c rim. In this case the BR-5500 arms are simply too short to place the pads fully on the rim, and not on the tire.

I'll rotate this photo when I get to my desktop. They are BR-5500

I have adjusted the pads every way I can. They're mounted as low as possible. In the photo above, the pads are just touching the rim on the front, but then they rub on the tire at their rear. If I set the pads level, they rub the tire in their center.
** I have switched pads from side to side as well. There seems no difference in the end result.

The front brake pads are fully on the rim. There's no issue there.