Yes, but it is the first step towards answering the question. Once you've clarified this (as per [MENTION=6690511]GX.Sigma[/MENTION]'s wonderings) you have a clear differentation between the two: If the attempt at disbelief is iniated by the PC, it's a Skill Check and if it's called for by the DM as a response to some effect, then it's a Save.
Now, my vote is for No. Skills don't give plusses to Saves, as they aren't iniated by the PC.
I understand how you're thinking about it, but IMHO it is a little dangerous to rely on the model (i.e. the artifact difference between a check and a saving throw) and the reality represented by such model. Because sometimes the model fall short...
For example, you cite "disbelief". I think that's an example of ambiguity of the model: how exactly do you "initiate" disbelieving? Is there really a difference between "active disbelieving" and "reactive disbelieving"? In the model yes, in reality not really.
Out-of-character (around the table) the difference may be real in the sense that maybe the DM asks you to roll so you can say that the player did not initiate, while another time the DM tells you nothing and the player asks "can I make a check to see if this is an illusion?". That means that whether it's a check or saving throw may depend on the DM even accidentally remembering or forgetting to call for a roll...
In-character the two are the same thing.
Another problem, take a Listen check when there is a noise that can be heard (opposed to when choosing to listen to a door "in case there is something to hear" which is definitely "active"): this is a "passive" check or "reactive" check, it's definitely the DM who calls out for a check here since the players could have no idea. Should it still be a skill check then, or should it be a saving throw because it's reactive?
I just want to point out that the model has its own shortcomings.
My preference is to use the model only when it solidly matches with
in-character reality, and otherwise just use common sense.
If you're worried about player's abuse, then I agree with you, and strictly enforcing the model has a benefit there. But there aren't that many skills IMO that can be used against many spells, so I don't think this can be easily abused, especially with the current "narrowness" of skills.
A "Sense Motive" bonus could be used in a saving throw vs a spell which lets the caster easily tell lies, but in fact such spells in the past usually granted Bluff bonues vs Sense Motive; but certainly "Sense Motive" shouldn't be allowed as a bonus to all illusion spells!
I think all this would be a better match with the current philosophy behind skills, which makes them loosely defined and detatched from specific ability checks. (But should they revert to a more strict model of skills, then I may change my mind and agree with you).