"They" have said not to take fish oils on an empty stomach first thing in the morning because, like you said, the EFAs may get burned as fuel. So it's generally best to pop a few capsules with a meal or [i]a little while[i] (a half-hour or so) before or after.
If we're talking about supplements besides fish oils, it would depend on what it is. I find HOT-ROX to work best on an empty stomach. BCAAs are also ideal between meals. And ZMA I usually take 20-30 minutes after my last meal of the day (along with some BCAAs, actually).
But something like a multi or other "non-bodybuilding supplements" are usually fine to take with food.