Well. In this case, the company could offer money, and maybe even contractual guarantees of continued employment. If structured properly these may be worth more than empty promises.
A person with a solid job that isn't on the chopping block (presumed because of the presence of a counteroffer) isn't job-shopping for a 10% bump.
Not so fast. I, for example never changed jobs for any other reason.
Of course, I never got only a 10% bump, but well, we do need money, and we should try to get more of it with time.