Do you have a source for this claim? I've never heard of this and I have read extensively on the subject. I have been part of the Deaf community, and I know people who are deaf, and hence their children's first language was ASL. Their children were still on target with all other children if they still had one verbal parent. For parents who are not Deaf, they speak and sign at the same time, so I don't know why the child would be delayed.

I have never once heard the claim that learning two languages at a time is anything but beneficial, regardless of what those languages are.