Nope, you're making up descriptions to suit your case, your premise only applies if gibberish means, "repeated sound, only differing in tone and length", which unfortunately, is not what it means.
Gibberish is simply that, unintelligible garbage.
Hufred inhag durwiig affo huiel.
Is gibberish, but could equally be Tongue.
Not enough data for me to tell, unfortunately.
Alternatively, you could link to studies to back up your extraordinary statement that people can't make up gibberish which fools linguists.
Actually, most of the citations that you would want would be cryptography citations, and I don't have them to hand. But it's fairly easy to demonstrate from first principles.
Rule #1 of quantitative linguistics. To a first approximation, everything is distributed as a Zipf distribution. Phoneme frequencies, syllable lengths, word lengths, and so forth.
To a second approximation, the mutual information between two separate linguistic objects vanishes after about five intervening objects (the citation here is, IIRC, Pothos and Juola, British Journal of Psychology; I don't know if it's on-line.) So at any reasonable distance, language is independent draws from a Zipf distribution.
Humans are lousy at making up "independent" sequences; this is well known.
So unless there's a language out there that violates every norm of cognitive linguistics and pays no attention to Zipf whatsoever --- which is possible, but only in the sense that we might find a colony of living T.rex's in a hidden valley in West Virginia -- humans can't make sequences with the necessary statistical distribution.
For further study of glossolalia, check out http://www.meta-religion.com/Linguistics/Glossolalia/contemporary_linguistic_study.htm
Another early study, that of W.A. Wolfram in the year 1966, also concluded that glossolalia lacks the basic elements of human language as a system of coherent communication.
The Zipf distribution being one of those elements....

