The better man? There is no such thing [base class]

[Necroticplague]

Not "combat maneuvers". Trip attempts and Bull Rushes explicitly call for a Strength check as part of them. Grapple checks are different, the grapple check is a modified attack roll, not an ability check.

The fact it says it is "like an attack roll" actually helps argue it is effected, since if it is like one, that means it isn't one. to quote the section you are thinking of:

Grapple Checks
Repeatedly in a grapple, you need to make opposed grapple checks against an opponent. A grapple check is like a melee attack roll. Your attack bonus on a grapple check is: Base attack bonus + Strength modifier + special size modifier

Or for possible less ambiguity, let's look under the definition of grapple check:

An opposed check that determines a character's ability to struggle in a grapple. Grapple check = 1d20 + base attack modifier + Strength modifier + special size modifier (+4 for every size category larger than Medium or -4 for every size category smaller than Medium).

Note this definition lacks both any reference to attack rolls, and explicitly calls it out as an oppose check.