I don't like it.
for several reasons, including:
saying character X is wanted for Y crimes in Z systems etc, to me, feels a bit like dictating to others, how competent the planetary entities are.
e.g. if someone claims to have escaped from things n times, then it makes Planet Z's police look like the Keystone Cops.
the Jita 4-4 chronicle, mentions how station police pretty much can kill any capsuleer they find outside the capsuleer section of the station, without any justification needed, because capsuleers = trouble more or less.
stating that character X can evade all this sort of thing time and time again, just seems silly to me.
"I landed on Pator, sneaked into Shakor's house and rearranged his furniture, so he'll trip over it" for example. If you were to accept that statement, then you agree that the Republic authorities, Shakor's security, and Shakor himself are by and large, buffoons. If you reject that statement, then it's far too easy to be accused of accusing people of "doingitwrong".
Of course, there is no obligation for a character to believe any other character.
If someone says they are a master of the Jin-Mei martial art of Dimac, the Iron Fist, the Invincible Way, and so on and so forth, then that is a thing that people have to agree to. It is not something that can be done unplanned or unconsensually. There is no way to make someone believe a character is a Dimac master if they don't want to.
There are a few things that are not ship-to-ship based where a character can do things.
If someone says they are an elite infiltrator, who has a huge network of contacts and agents across new eden, then no-one is under any obligation to believe them. That sort of thing can be acted upon though, however if the characters actions extend only to petty corp theft and hiring highsec-based mercenaries against 0.0 based individuals, then that is a bit daft.
it is depressing.
There are ways to become recognised for inspace things that do not necessarily include kill/lossmails, and then a character becomes "Hey, it's (name)!" and people know who they are and so on.
overall, vOv. People can do what they like, as long as they realise that others don't have to believe them, and may call them out.