Not at all. First assume that there are two players of equal skill (tactical ability, mind games, etc) and equal reaction speed competing in a 1v1 game that requires fast reaction, eg. a first person shooter. Reaction time will be variable, and it will follow a probability distribution. This won't be normally distributed because there's a fixed lower bound (call it 150ms), maybe something like log-normal distribution. Something with fairly heavy skew, finite lower bound, infinite upper bound.

Because the gamers are concentrating hard they will be mostly operating near peak reaction time, so I don't expect much variance. Now if we offset the distribution curve of one of the gamers by 16ms, and look at the difference/intersection of area under the curves:

(p)
|  __ __
| /  X  \
| |  |\__\__
|/  /%%%%\__\____
|__|%%%%%%%%%%\_ \___ (time)

The unshaded area is guaranteed win for the unlagged player in a mutual surprise situation. This matches what happens in server side hit detection FPS, where the "LPBs" almost always win when 2 players of equal skill surprise each other. 16ms might not be much compared to 160ms, but it is compared to the variance of reaction time, which is the important thing. These small differences in lag do have a significant gameplay effect, which is why almost every modern FPS now uses client side (but usually checked on server for anti-cheating) hit detection.