So I sent an email to the director of the University of Arizona Triga reactor to get some clarification on what is going on. I provide the link I posted earlier so he knew what I was looking at. Here is his response;
"Justin,
The information in the link you sent is reliable, though the model he
describes is known to me as the Fuchs-Nordheim model, not Fuchs-Hanson.
There is a small Doppler broadening effect in TRIGAs, the reduces the
resonance escape probability as in other thermal reactors, but that is not the main
contribution to the negative temparature coefficient. The main contribution
comes from a spectral shift of the thermal neutrons. Because most of the
moderator is homogeneously mixed in the fuel, its temperature is the same as
the fuel temperature. Therefore a rise in fuel temperature increases the
neutron temperature of the Maxwellian part of the spectrum. Because the
fission cross section in uranium is approximately inversely proportional to neutron
speed, the higher the neutron temperature, the less the effective
fission cross section. This reduces the thermal utilization, eta, and hence reduces keff.
There is no comparable effect in reactors with the moderator separate from the
fuel."
Justin