Mmm, yes filtering might be a good idea. Also, running a thick wire conductor from the case (metal?) of the radio/and/or BNC shield to a good Earth ground (grounded water pipe or stake) might help with decoupling. If you happen to have a ground rod and a long piece of wire and alligator clips, you may give this a "try".
edit: Another thing I wanted to mention...I don't know what kind of resistor you decided to use, and it may not be altogether important, but I suspect your resistor has a series inductance (and by nature a parallel capacitance too), but the inductance is the primary reactance at 100 MHz. Your supplied antenna is an "open circuit" type of antenna, thus capacitance tends to be the primary reactive component. The dummy load more resembles a "loop" antenna, (thus the inductive quality) Both will radiate, but an inductive antenna (or inductive dummy load) will radiate a stronger magnetic field whereas the capacitive antenna will have a stronger electric field. An ideal resonant circuit will have equal energy in both fields and will radiate "electromagnetically".
Both magnetic and electric fields can cause EMI of course, but stronger magnetic fields, for some reason, tend to couple to other electronic devices and are more susceptable to coupling themselves. I think this is because of the angle of the radiation for magnetic vs electric fields. Electric fields are perpendicular to the axis of the conductor where magnetic fields are more or less parallel (lines of flux with varying densities etc) Because of this, the device receiving electric field interference is only receiving it on a perpendicular axis whereas magnetic flux lines "will find" a parallel conductor in the device and induce currents.
I think this is as good an explanation as I can jog in my mind at the moment for why you are causing EMI.
If we knew just how much inductive reactance is occurring (I'm quite certain it isn't much), we could calculate a value for a parallel capacitor to null it and reduce the magnetic field you're creating. I own an antenna analyzer that does this very thing, it looks at the load reactance and calculates the frequency of resonance and can indicate the degree to which the antenna (or dummy load in this case) is capacitive or reactive.