You are also correct that not all balanced outputs/inputs indicate truly balanced design. In fact, it's probably not "some" but "most" outputs that are not truly balanced. Companies such as BAT (Balanced Audio Technology) do build fully balanced designs whereby there are complete circuits for both the pos and neg "legs" of the run. Keep in mind that to leverage balanced, everything in the system, from source to amplification should be balanced. The primary benefit for full balanced is when there are long cable runs (which become antennae) a balanced line will cause interference introduced by this antenna effect to self cancel. I believe that balanced design may also enable the signal voltage to also be higher. You don't mention the lengths of your runs, but if you have a long one, then balanced may solve the issue.
If, on the other hand, your hum is a ground loop, this will make no difference. Spencer makes great points, especially concerning TT--I would add that if there's any cable TV, satellite or other video-oriented sources where RF cable is involved, they can be a source as well.
If, on the other hand, your hum is a ground loop, this will make no difference. Spencer makes great points, especially concerning TT--I would add that if there's any cable TV, satellite or other video-oriented sources where RF cable is involved, they can be a source as well.