The linguistic part to this question that I can see is, what is the phonemic or phonetic quality of "r" in US English? The cites answer answer correctly challenges the erroneous transcription with /ʀ/, however attributing phonetic properties to phonemes is a tricky proposition (though people do it). There is no phonological fact suggesting the "r" is phonemically /ʀ/, and no phonetic fact suggesting that.
The standard most-phonetic IPA transcription of that sound would be [ɹ] (probably actually [ɹʷ], at a finer-grained level of detail). In lieu of compelling reasons for making the phoneme distinct from its allophonic realizations, "r" would therefore be phonemically /ɹ/ – if you want to adhere to the widely-adopted principle of using the nearest IPA letter. The statement that this "r" is velar or uvular is correct-ish, that "r" in US English is not equivalent to /ɹ/ found in a number of languages of Nigeria (I believe Yoruba has this feature), also I think Carribean English. The approximant of US English is a high back approximant, which given a theory of features would be taxonomically called "velar".
I would not trust speaker reports of what they do unless them come from John Esling (a well-qualified phonetician and expert in such matters, who is a native US-ish speaker (I don't know where he was born and raised, could be Canada). Perhaps there is some quantitative evidence in the literature that addresses the "retroflex" vs "bunched" distinction, but that seems irrelevant to the answer that you're asking about, since he makes no claim about that.