I can confirm this issue as well, for Minecraft 1.7.4.
I replicated this issue by manually timing how long it took for the score to reach 60 when crouching, walking, and sprinting. If the score actually incremented with distance, I would expect each movement to take different amounts of time to reach the same distance score.
However, each took the same amount of time (~3.44 to 3.45 seconds), which comes to 0.057 seconds per score increment.
I am glad to see this issue is being tracked; without the ability to set objectives when players are offline, there is no other method (to my knowledge) to test for when players leave mid-game in pvp maps.
Also confirmed, MC 1.7.4.
This is the second issue I've run into today with stats. You get similar issues with stat.walkOneCm, as seen here:
https://mojang.atlassian.net/browse/MC-39139
I'd like to build a map based on The Hidden, but if the monster takes fall damage then there is no point continuing with the build. You can use resistance effects, but it also means the monster is resistant to pvp damage. If there were a fall damage status effect, a lot of this could be mitigated.