Wasn't MAX pretty huge at the time of Ayu's debut? Not to say that they did it or anything, but they come to mind as a popular avex girl group and "Axel's" could come from MAX -> LAX -> AXL and somewhat fits their weird renamed OTF/Over The Fact/ELT/Every Little Thing, usg/TRF scheme. Especially the TRF one since it just uses the letters after "TRF" to make "USG". The other group I saw as a guess was SPEED but they don't really fit the name as well as MAX.
I am sure Ayu was bullied by TV execs and stuff but some of those other artists? She seemed on good terms with Yuki whenever they did have to interact but with regard to hitomi, the 'rumor' maybe came from when hitomi herself actually did comment a bit about Ayu on a talk show and it seems they were not close at all or the relationship was very distant/delicate?
https://news.livedoor.com/article/detail/10910455/