First question is; what does it mean "near"? for example, I have a plum tree to 3.5 meters from a big fig tree (10+ years, 8" trunk diameter) and I haven't noted any damage for the plum tree.
Another thing is the shadow of the canopy, obviously, some trees under the shadow of a big fig tree won't grow well, but it isn't a peculiarity of the fig trees, all big trees do shadow.