How should a graduate admissions committee view (possibly false) accusations against an applicant?
If I were the head of the grad admissions committee (which I have been in the past) and either an anonymous or signed but unofficial email came to me or a faculty member, I would:

1) if the email is from an email address that is reply-able (or from a person who is googleable), I would write to them and request they make an official statement. I would also double check whether the email is actually the one from the person it denotes. 

2) if the email is anonymous or the email address doesn’t match, I would instruct faculty to ignore it. 

3) however, in either case it’s my responsibility to inform the graduate school that we’ve received derogatory information of unknown provenance. The grad school will likely tell us to ignore it but I need to cover my ass. 

In reality, I’ve reviewed well over a thousand files in my decade plus of teaching at the graduate level and haven’t yet received one of these notes. Most faculty if they have something to say, are not shy about writing it in the main letter themselves (whether in coded form or outright).