The lightgrid (which lights player models) is generated to q3map2 so this is a q3map question.
A smaller gridsize might help, but it looks like the the player really shouldn’t be that dark at that point, so it would be better to figure out what is wrong. I’m not sure how much impact it has on runtime peformance (likely some) but it can add a lot to bsp size, and if you have more than 8 megs of lightgrid data, the light compile will fail.
Some compile options also affect the lightgrid lighting, maybe playing with those will reduce this effect. Which version of q3map are you using ? and what options in the light compile ?
In any case, you might want to take a close look at the brushwork in that area.