Phones are generally blacklisted just by carriers, if someone was to try to blacklist a phone, they would need to have it active on their account, and if you have it active on yours, then no one else can have it active on theirs, and thus can't blacklist it.
If a carrier blacklists a phone for someone simply by request without any confirmation that they in fact own it and have it as part of their account, then it sounds like it's a bad/incorrect practice of the carrier (or at least the representative that would do it) rather than anything else.
The problem is the phone can be blacklisted by the carrier themselves. If i get a phone on contract and then sell my phone to another person, and then dont pay my bills and my account is suspended the carriers can blacklist the phone. People have bought used phones that work for a month a two and then get blacklisted.