It seems like they do, yes. A few things factor in to this, too.
- Pros play faster greens, so even with the same capture speed, the ball will roll out farther.
- Rarely are pros putting from 3-4 feet after missing from 4-10 feet. You're relying on memory, while Broadie has stats (it's basically 1.2 to 2.2 feet on average, depending on whether it's uphill or downhill).
- Some pros don't understand the benefits of a slower capture speed. They ARE pretty good putters (though not nearly as good as people often think), so they can get away with smaller margins of error, but they also only make 96% of their three-footers. Phil Mickelson stands out as the good example here: he jams short putts quite often, and lips out quite frequently too.
Not to debate the rest of what you said (because, except for the frequency of the time they hit it 3-4 feet past, which you only even lightly implied, it seemed fine), but this is true… but not by a lot. Something like 1% of five-footers on the PGA Tour are left short versus 3 or 4% for even lousy amateurs.
I wasn't really talking about them missing a putt by 2-3 feet, could be anytime that they have 2-3 foot putt, sand shot, missed putt, chip, stiffed wedge, whatever.
I think most of the time, we only see the guys making everything on tour or when the leaders or stars miss and we don't see the 30 other putts that they took, so you go by what you last saw and sometimes we forget everything else.