For the reasons stated, I would not give in. This is a slippery slope.
Raising the pay of one employee out of band will usually lead to group behavior, meaning others do the same for the same reasons. I was also mostly budget constrained in the past and could not raise budget to significantly (say 20%) pay raise several employees.
If the employee for whatever reasons earns say 10% below average of the other employees, I would get her a pay raise.