The simple fact that you aren't willing to offer any evidence when asked for it does in fact make you and your assertion appear to be a lot less credible. This is public data at least anywhere in the US. Where is this largish hospital? Inquiring minds want to know.
Is it public data anywhere in the US? I know that my state (Michigan) doesn't break down hospitalizations by vaccination status. Or if they do, it's not with the rest of the Covid data they put out online.
The link below suggests that the story your doctor acquaintance is telling telling is either an outlier for your state or is just incorrect. BTW, I found this data from last week with this search "us hospitalizations covid vaccination status". There's also CDC data which is updated weekly that can be seen in the same search. So not hard or complicated to verify.