"Can" gain support? In what bizzaro universe would the Chinese government not support this bill?
The ambassador's comment was the only thing he could have said, really. I.e. that it is not for the central government to draft HK legislation.
It's not a question of supporting the bill but of question of supporting the HK government despite the unrest it will create.
The Chinese government may conclude (and may have concluded) that at the moment there are much more pressing problems and that they could do without riots in HK.