So the answer is yes. And I think the outcome is as I described.
Let's say that Player A is 25% likely to succeed, and Player B is 50% likely to succeed.
If they both succeed, it's true that Player A is twice as likely to be the winner, even though they have the lower skill. But they are both going to succeed only 1/8th of the time, and of that 1/8th, A will win 3/4ths of the time. So that's 3/32 wins for A, 1/32 wins for B.
And another 1/8th of the time A wins outright because they succeed while B fails. (0.25 * 0.5). A is up, 7/32nds to 1/32nd.
But wait! Another 3/8ths (0.5 B succeeds * 0.75 A fails) of the time, B succeeds and A fails! So, regardless of the actual value on the die, that's another 12/32s for B. Now we're at 7/32 for A and 13/32 for B.
So, really, you are more likely to win with a higher skill, even though it's true that "if both succeed, it's probable that the person with lower skill also has the lower roll."
(Again, unless I'm misunderstanding how the rules work...)