Even at schools that have MSTP funding, the training grant pays for only a portion of the students being trained. The average last year was around 25%, with a range of 10% to 45%.
The reason you would consider a non-MSTP school is because all MSTP schools were non-MSTP programs before they received the MSTP grant. In order to be competitive for funding, they needed to have a profile that mirrored MSTP institutions in terms of competitiveness of the applicant pool, quality and quantity of research opportunities, organization & integration of the program, administrative and financial support, attrition, student publication records, program outcomes, etc. Obviously, they are not expected to look like Harvard, but they should resemble other, humbler MSTP schools. A program needs to operate at the level of a MSTP for 10 years to have a realistic shot at being funded.
With the cuts imposed by the sequestration, it would be risky to not consider applying to non-MSTP programs, especially if you have a strong preference for location.