In that case, it seems like a perfectly reasonable culprit. I would check the power supply line to the 10MHz source, but there are some less invasive things to try. Fields can induce the hum in wiring, but the SA should be plenty shielded and the BNC to connect the two should be reasonably shielded as well... so my guess would be it's getting into the signal before it arrives at the SA.
If you can look at the 10MHz signal on a scope to verify (high resolution mode, FFT) that there are the same tones in it, then it would at least take the out of the list of potential culprits. The SA could also do this (measure the 10MHz reference output without being referenced to it), but it's nice to have a neutral third party to measure, and -50dBc should be measurable on a modern scope FFT.
Then maybe check the DC resistance from the shield of the BNC for the reference to the chassis ground for the sig gen, and maybe check the resistance of the ground pin of your signal generator, if either is sort of half-floating because of a poor ground connection, this sort of hum can be picked up on a shield instead of kept out.
While there are some people that like isolation in their 10MHz reference distribution, most commercial distribution amps don't use it - since the signal is fairly large and fairly pure, just filtering it on the input side can keep out a lot of the potential noise, so elaborate grounding and shielding measures are usually not used or required.