I know plenty of non musicians who can guess time to within 15 minutes so that's more of a human thing I think.
One thing musicians have that mere mortals don't
is the ability to sort of dissect music and figure out what's going on to a much higher degree than your average bear....or so I've been told. Some musician probably made that up.
But back on topic, good musical time is something that can definitely be acquired if you don't have it. I know because I definitely didn't have it for a LONG time, but I'm far ahead from where I started from, mainly thanks to listening recordings and most importantly, adjusting, and proper tempos are always one of the most important concerns for me...it's something you never stop refining, this 6th sense meter/tempo feel we try and develop. I should just record the tempos and let a metronome count me off but I want to
feel the perfect speed for a song without any help. I'll let you know when I'm there lol
Actually if you really want to get at the heart of the topic, good sense of time...time to me means meter, keeping evenly spaced quarters from start to finish. Tempo on the other hand is where a good part of your feel lives. If you play it too fast, too slow, a lot of songs feel "off". So tempo deserves honorable mention.