The application of salary money  from a grant is to release the time of the grant holding PI to devote the % of time to the project  as agreed by the terms of the grant. Since the time replaced was, usually, from the program of the educational institution, the decision about how to cover the lost function lies with the institution.  Most institutions have fought over these "bones" before with the outcome dependent on the exisiting institutional culture, i. e., the money "belongs to":  the University(President); the College(Dean); the Department (Chair); the Research Component (Institute Director; and rarely, last and least, returns to the PI's  benefit in such a way that it does not violate grant guidelines in such a way as to inflate the PI's  income.  If you have to ask in your institution the wounds of earlier battles may have healed.  In some cases Prof. $$$ may have so many grants associated with a specific project, institute or high profile as to "command" a special status with the officials listed above which "justifies" an exception to  the usual policy.  You might check it out by asking to run a question by your superior in the budget tree, chain of command or food chain to get their "initial " response.  The PI's assumption  is often too self focused to be sustained by the larger realities of administration of the research resources for the greater numbers.