I wouldn't, myself, say that we sport Rocky the same speed. I don't actually know how fast Rocky is.
But the whole business about arrow catching is that it IS timed, it IS set up at specific distances, and it IS practiced. Kind of like this seems to be. I scrolled through youtube looking for examples (like one dude who basically catches a ton of arrows, one after another). Now, while the Daikyu is probably more powerful than the bows I've seen people using to do their arrow catching (modern Kyudo stuff tends to be in the 30 lbs range, which is better than a 20lbs target bow...but not really 'strong', if we're talking about 'strong bows'),
the monk doesn't bring the arrow even close to full draw (2:45) and it's at a fair distance (longer distance than we see with most of the 'arrow catching', aka something I would be happy to name 'arrow timing' in this case, because that's exactly what it is).
Heck, there's a guy who catches arrows blindfolded. Timing, again.
What I'm getting at is that while this is impressive, I'm not myself hyped on the idea that it means Miyagi is blitz-fast or something. Especially since every 'arrow catching' I've seen is set up exactly like this...and ends up being because of timing. If it were in an uncontrolled situation, sure, I'd be fine with it being 'dude can catch arrows solely based on reflexes'. But it's not.
Mileage, it may vary.
Edit: to clarify, I'm not crapping all over this feat. Dude has to have some good reflexes. I'm just saying that one arrow-catch, in controlled circumstances as noted above, which would probably also owe a big chunk to 'timing', is not, for me, a good indication of some kind of amazing speed. I'd want more.