The vases in the link look ok to me - the metal grabber is made with an opening to gently push the glass into - normally they would be in a closed fused circle of metal with the glass sliding into it from top (thinking epergne cone shaped glass e.g.).
The whole thing reminds me of a Bagley 50s or 60s type piece, perhaps it is an Italian version thereof? Or maybe it is a Bagley type stand that was made to have three Bagley bits in it and someone's replaced with the Italian vases?
But I think it looks ok
m