3 to 100 times Earth background is not a lot. The world average is about 3mSv per year. People in places like Ramsar, Iran have a yearly dose of up to 260 mSv with no reported ill effects. You will need to bump that up even more so you end up at around at least 1 Gy/year. But that is just petty details... you can pick an arbitrary number.
To your question: the beneficial effect would be...
- the symbiotic partner can make use of the fungi's DNA repair mechanisms. Some species have exceptional DNA repair and can survive massive doses thanks to that. The bacterium Deinococcus Radiodurans ("Terrible berry that endures radiation") can survive doses of radiation that are 5000 times higher than what causes acute radiation sickness in a person.
In your universe, you can have a fungi that allows the symbiotic partner to make use of this repair mechanism for themselves.
- the fungi can have a shielding effect by hosting substances that have a high nuclear cross section. This would be useful if you had natural neutron radiation.
EDIT: As requested, let us go deeper into this.
Actually what you wrote in your original post is hitting close to the truth already. There has been some interesting research results from the Chernobyl area that suggests that animals can actually adapt to a higher-than-normal radiation environment. And it is assumed that anti-oxidants is the key.
Bank Voles - who have now bred for over 50 generations in the area - show no ill effects of living there. They even show slightly higher then normal resilience when subjected to even more radiation. It is thought that anti-oxidants play a key part in this. The radiation is causing oxidative stress and the vole's body responds with producing more anti-oxidants (or as the article suggests: producing less of red/pink pheomelanin that otherwise use up anti-oxidants). You can read more about it here.
In your world, the fungus may have its own version of photosynthesis - or in this case perhaps we should call it radiation-synthesis - that make use of the highly energetic radiation photons to produce a surplus of particular anti-oxidants that can be absorbed by the symbiotic partner and put into use to defuse the free radicals caused by radiation before they can damage DNA.