I can believe that a person might genuinely think that a certain form of "speaking in tongues" is real or valid, but this is where the subjectivism of the form comes into play. Objectively, the Bible never says that speaking in tongues was done with "gibberish". Those that spoke in tongues were understood. It would be akin to out of the blue you suddenly mastered the Russian language.
I'm also confused as to what "the language of Angels" is supposed to stand for as all angels in the Bible speak to man in his language. If I'm missing something, then I'm missing something but I don't think there is any biblical mention of an angelic language.
I, also, don't want to call anyone as a fraud, but as Christ flat out told us, many will come "claiming" to be prophets, "claiming" to come, or speak in His name and that we are to "test" these people for validity and the Bible does an excellent job in giving us a checklist, so to speak, for such a test. If talking in gibberish is biblically supported, then I would be interested in the reference. If not, it could be implicit, but again, we need references for that. If that's not possible then you have to concede that gibberish is not speaking in tongues.