Hrm, if her daughter is throwing a strop about it, then she clearly can't back down.
Having said that, more generally I would say 'it depends'.
I read some a lot of quite challenging porn novels at that age or shortly thereafter. Thing is though, they weren't the first novels I read where I encountered sex scenes or other adult material.
Like others I read James Herbert, crime novels etc. My father actually bought me a copy of Fanny Hill when I was about 14. He had no issues with my 'banned books' stage
as he'd had one himself. I am now settled with my partner of 10 yrs, have a nice house and a good job 
One thing I would say is that all my adult books were either historical, fantastical or specifically badged as horror. I do wonder if that helped at that age because none of the behaviour in the books was normal, so I doubt they normalised anything unhealthy, because very little in the books was 'normal for me'.
I've not read the Grey books, so can't comment specifically, but I believe they have a modern, morer plausible setting so that might be a bit more difficult.