All modern radio receivers have an inbuilt oscillator, which generates a signal to create an intermediate frequency. At very close range this oscillator acts like a very low powered transmitter. The weak signal does not require the same standard as an ordinary transmitter, and it probably has a lot of harmonics, and other unwanted characteristics. The unintended transmission by your radio, and reception of these oscillator signal signals by your GPS is likely to be the problem.
Incidentally, the reason why your radio is not adversely affecteed by its own oscillator is due to design and careful selection of the oscillator and IF.
Check this out. Tune an SSB signal on an AM shortwave radio. random tune another radio positioned in very close proximity. The oscillator harmonics of the second radio can beat with the SSB signal to enable you to understand the signal.