In terms of subjective perception, I believe he thinks it is a clean, articulate sound rather than a sluggish or muddy sound. Personally, I don't really like the term "fast". Is it in HP's glossary of audiophile terms?
"Fast" is in Gordon Holt's The Audio Glossary: "Giving an impression of extremely rapid reaction time - of a reproduction system being able to "keep up with" the signal fed to it. Similar to taut, but applied to the entire audio frequency range."
Or Gordon Holt's "Sounds Like? An Audio Glossary" which is online: Giving an impression of extremely rapid reaction time, which allows a reproducing system to "keep up with" the signal fed to it. (A "fast woofer" would seem to be an oxymoron, but this usage refers to a woofer tuning that does not boom, make the music sound "slow," obscure musical phrasing, or lead to "one-note bass.") Similar to "taut," but referring to the entire audio-frequency range instead of just the bass.
I agree with you - I don't like the term either (though in 2008 I did use it in a review.) As used in audio talk "fast" seems unclear in terms of the object to which it is applied.
As we see with Holt and some responses here, the word gets described by its synonyms. Though Holt does say "Giving an impression ..." which suggests something subjective. The folks referring to speaker rise time or settling time suggest an objective event or measurement as a cause? of such impression.
I am inclined to agree with your audiophile friend's "clean, articulate sound" though I might say "clear and distinct". As @Tim Link suggests above, I do not hear live acoustic music as "fast" in the same sense as the word is used for audio systems.