That doesn't make any sense. At least in the USA, if the school is paying you then they have to issue you either a W-2 or 1099, regardless of whether they label it as a salary or stipend or whatever. Mortgage lenders are accustomed to verifying income from sources like that, it's not complicated.
Here in the UK a 'stipend' from EPSRC or similar is not classified as income for purposes of income tax or council tax. It's treated more like a scholarship.
> That doesn't make any sense.
Tell me about it. They still won't give you a mortgage, though.