Fellowship replacement when new fellowship is lower?

[jriveracal]

Does anyone know how this would work?

An institution notes: All students who receive funds from an outside source are required to accept the award in place of the award we are offering you. In such cases, students may be eligible to receive an award of up to $4,000 for each academic year of external funding secured.

The school is offering me $35k/year. [30k academic year, 5k summer]

Let's say I apply for a ford foundation predoctoral fellowship and receive it. The stipend is $24,000/yr. +4,000 a year from the institution for securing an external fellowship=28,000/year
So if they replaced the fellowship they are offering me with the fellowship I received...it would be significantly lower. 

Am I missing something here? Am I supposed to only apply for fellowships that would offer me more than what the school is offering me or...?

[high_hopes]

I think generally universities with these types of policies will pay the difference in funding if you receive an external award that is below their own guaranteed funding level. So in your example they would provide $11k - as the difference between $35k (guaranteed) and $24k (received externally). This might reduce the amount of TA or RA hours you are expected to complete if that was part of your funding offer.