Supposedly the ability to guess how long a minute is also goes that way as you get older, e.g. older participants think a minutes is over after 62s or more. So if your internal clock slows down a B would sound like a C.
I've been playing music for thirty-odd years, and I couldn't name pitches by ear most of the time, certainly not without thinking about it. I often hand-tune guitars (relatively!) if I'm playing by myself, and after a few days of that, it's not unusual to be more than a half-step out of whack. I don't notice, because it's in tune with itself.
You can still hear and appreciate music, but you can't whistle or hum along to a tune.
I don't get it!
There are links other possible theories on that page, namely the temporal theory, which does propose we rely on neuronal clocks. It seems likely to me that both theories play a role in pitch perception.
I'm out of my depth here, but wouldn't that process still require some kind of 'clock' (albeit not necessarily the one used for conscious time perception) in order to resolve the signal into absolute, rather than relative, frequencies?