Byrd has not been quite right since being beaned by Aceves last June. Had a .230 AVG after that. He also dropped 40 lbs this off-season, for what he says is health reasons, but might be because . . . well, his personal trainer was tied to BALCO. Maybe Rizzo has a right to be skeptical.
Bourn would have been the White Whale, while a Byrd move would have been short term patching. It is different, I think. Maybe Rizzo has a reason to be skeptical, but Byrd has had a very good track record up to this point.