The scores all seem to indicate that would be true, the top skaters without quads need the top skaters with quads to make big mistakes or do an overall real sloppy program, and then to either skate clean or make far less mistakes to have a chance to beat them in the scores.
Well, but how do you define "top skaters"? To a large extent it has to do with basic skating skills and with the quality of the elements including the jumps, not just what jumps they're doing. But it will be a continuum -- however you define a given level of skating, there will be ranges of ability within that category, and the best overall skaters in the category may be able to defeat someone with lower overall skills who happens to outjump them.
It it same in womens probably. All girls with triple-triple will probably always beat girls without one.
No, not always. Look at 2005 Worlds short program, for example. Two skaters who skated clean with triple-triple combinations, who had the highest jump scores, finished 4th and 7th in the short program. The skaters who placed ahead of them had lower jump content and in some cases more serious (but not disastrous) mistakes on one of their jumps. It was on the non-jump elements and the component scores that Kostner and Ando found themselves behind the leaders.
Let's look at a hypothetical men's short program, because there's less room for variation in the jump content than in a long program.
Skater A's jumps might be triple axel (7.5 base mark), solo triple lutz (6.0), and quad salchow-triple toe (9.5 + 4.0 = 13.5), for a total base mark of 27.0 just for the jump elements. Let's say he lands them all cleanly but the quality is only average and the grades of execution average out to 0, so he ends up with 27.0 total for the jumps.
Skater B doesn't have a quad, so he does triple flip-triple toe combination instead (5.5 + 4.0 = 9.5); the other two jumps are the same as A's, and his jump base mark is 23.00, or a total of 4.0 behind A on the jumps. But maybe he goes into his jumps with more speed, he jumps higher, he's straighter in the air, and he carries more flow on the landings, so his grades of execution average +1 on all three jump elements. That would give him another 3.00 for jumps, for a total jump score of 26.0, only 1.0 behind A.
It's very easy to make up 1.0 difference, or even 4.0, with some combination of higher levels on the spins and steps, better grades of execution on spins and steps, and higher component scores. If B is better than A at any of those areas, especially several of those areas, B will probably come out ahead when both skaters land all their jumps.
What about long programs? There are more variations in how skaters can choose which jumps to do and how to arrange them, but let's try to keep the jump layouts as similar as possible with the exception that skater A has one quad in his repertoire and skater B has none. Let's stick with the quad salchow to increase the point advantage, although more quad guys are doing quad toes.
The men are allowed eight jumping passes, which may include up to three combinations or sequences with two jumps each, or one combination can include three, for a maximum of eleven jumps. They're allowed to repeat only two triple or quad jumps one time each. To simplify the calculations, let's assume that both these guys use all the jump slots allowed and neither of them does a jump sequence, and we'll ignore the multiplier for jumps in the second half of the program.
So, maximizing the allowed jump content, A's jump passes might be (not necessarily in this order):
13.5 quad salchow-triple toe
9.5 quad salchow
10.3 triple axel-double toe-double loop
7.5 triple axel
6.0 triple lutz
5.5 triple flip
5.0 triple loop
6.0 triple salchow-double loop
Total: 43.3 jump base mark
B's could be:
10.3 triple axel-double toe-double loop
7.5 triple axel
10.0 triple lutz-triple toe
6.0 triple lutz
5.5 triple flip
5.0 triple loop
6.0 triple salchow-double loop
3.3 double axel
Total: 33.6
Difference in jump base mark is almost 10 points. If B can average one point higher in grades of execution for all eight jump passes, he can close the gap significantly just within the marks for the jumps.
Otherwise, the differences in base scores and the values of the GOEs for spins and steps are lower than for jumps, so it's harder to make up as much ground there, but if B is a better spinner and/or better skater he can get higher levels and higher GOEs and gain several points there as well.
So it would be possible to make up the difference in jump difficulty just by doing all the jumps better, AND doing harder spins and steps, AND doing them better.
OR, as pointed out earlier, the component marks are multiplied by 2 in the long program. So if B can average 1 point higher on every component (e.g., 7s to A's 6s), that will more than make up for the jump difficulty right there.
If A and B are close in overall ability, then yes, A having a quad will work in A's favor when the rest of the scores are close. But if B is a better skater overall, there are many ways to compensate for A doing harder jumps.