It's pretty clear that the top four are a notch above everyone else. This is a mathematical look at their relative ranking. If anyone wants a more detailed explanation of my premises/setup I'll give it later.
Since the tier list is supposed to control for individual skill, the outcome of any given match is a probability.
Going by some pretty commonly accepted matchup values (dittos are obviously 50-50):
Fox:
vs Marth 50-50, vs Sheik 55-45, vs Falco 50-50
Marth:
vs Fox 50-50, vs Sheik 45-55, vs Falco 55-45
Sheik:
vs Fox 45-55, vs Marth 55-45, vs Falco 50-50
Falco:
vs Fox 50-50, vs Marth 45-55, vs Sheik 50-50
It's pretty immediately clear that since Falco's matchups are strictly worse than Fox, there's no reason to play Falco under the assumption of equal skill.
Removing Falco, we get:
Fox:
vs Marth 50-50, vs Sheik 55-45
Marth:
vs Fox 50-50, vs Sheik 45-55
Sheik:
vs Fox 45-55, vs Marth 55-45
Therefore the expected win value for each character would be:
EVfox = .5*F + .5*M + .55*S
EVmarth = .5*F + .5*M + .45*S
EVsheik = .45*F + .55*M + .5*S
where F is the percentage of Foxes in the metagame, M is marth, and S is sheik.
A stable metagame implies that each character's expected value is equal to 50%.
So you get a system of equations
.5*F + .5*M + .55*S = .5
.5*F + .5*M + .45*S = .5
.45*F + .55*M + .5*S = .5
where F, M, S are between 0 and 1.
since .5*F + .5*M + .55*S = .5 = .5*F + .5*M + .45*S,
.55S = .45S
This means that there can't be a stable metagame with Sheik in it, i.e. Sheik is not as good as the other two characters. (Even if for some reason there are a ton of Marths at first, the Sheiks will beat them out and eventually it will be a few Foxes and a lot of Sheiks. Then the Foxes will beat the Sheiks out, and it's back to Fox/Marth.)
therefore S = 0, and you get a stable metagame of 50% fox, 50% marth. (or, more precisely, a metagame where its irrelevant whether you're fox or marth.)
Final Result:
Fox & Marth tied for 1st
Sheik
Falco
in that order.
The result based on those matchup values seems to be supported by tournament results.
The only way Sheik would end up being first or tied for first would be to have her not at a disadvantage to Fox, or have Fox at a disadvantage to Marth or Falco.
The most accurate tier list would be the one calculated from the most accurate matchup values.