Not really anything there to justify calling him a liar.
Let's agree transferring internally domains (push) may be possible without controlling (initially) the registrant email address. I guess it would be usually nottoo easy (I don't think very highly of GoDaddy). This story seems unlikely to me in term of probabilities. Especially for it to happen with 3 different registrars. No mention of a complaint to the registrars, nothing (no mention of the names stolen for people to look out for their resale either). And there is probably a bias from my part related to a previous story he was involved in. Anyway, this is solely my own opinion. I can definitely be totally wrong. If I had to bet, I would personally bet the alleged story (as it is described) is mostly fake. Again: I can very well be wrong. Only my assessment. - I do respect your view.
@base I am asking myself if it depends of the registrar? It's crazy because I have done quite some pushes recently and I'm incapable of correctly remembering the email validation part (or lack thereof). I believe some (most?) did ask for a validation by email. But I may be mistaken, or confusing it with some external transfers (Auth codes). I will try to better look at what is needed during the next ones. I encourage you and others to do the same.
I believe I've seen some recent discussion here about the lock of the domain after a push. Some people were (understandably) not very happy about it. But for this kind of situation, it does give the opportunity to the victim who got his domain stolen to complain to the registrar during the lock period (the domain can't get out during that time).
I don't know how frequent domain "stealing" actually happens. I know we hear sometimes about it (maybe more on the people warning about it or selling a product against it, than actual cases?), but a domain can be tracked easily. It seems difficult for the person who get it to do much with it. The victim should just inform the authorities. Stealing is still illegal, whatever is stolen. It seems a little difficult to get away with it, in the end (and to use the domain).
But it may be interesting to study how feasible it would be registrar by registrar. If there is no specific rules for pushes, where can a domain be pushed and transferred out immediately, without any registrant email validation, and where is it impossible (because of email validation and /or lock period). Maybe there is a case of more or less secure registrar in that regard (having your domains potentially stolen). Or has this already been done?