I also think this is a decent way to examine the question. I'm going to assume some training is allowed, because obviously with no training the percentage is going to be LOW. I'll assume male, 25, body fat reasonable; so 12% or so.
We know that as a general rule of thumb you can get a guesstimate for 400m ability by 2(200m +2s), or 4(100m + 1s).
So to run a 400m in 60s it's looking like you need at least 14s speed. However, that formula tends to be more applicable to faster folks, so let's call it 13.5 here. Somewhere around that is probably the average 100m speed necessary to run a 60s 400.
My guess is that given my original stipulations, average 100m ability is around 15s, give or take half a second. I don't know the distribution, but 13.5 is dramatically faster than 15, do for my upper bound I'd say around 10%. That's probably overly generous, and I suspect that actual result is somewhere in the 3-5% range.
If we really had a good idea of average 100m ability, or of the distribution of sprint speed, then we could make a much better estimate. However, there is no way in hell it's a majority without assuming years to train, and even then who knows.