It's not so hard to imagine. Just think of the loop between the cable (as a single lone wire, ignore the fact that there's more than one wire inside there) and any kind of ground return (which can be space itself, but is often some other powered or grounded equipment coming back through the power line or ground). Thus, anywhere you have CM current along a cable, and a poor shield on that signal (like the ground clip, rather than the shield being 100% wrapped around the signal line), you get some voltage drop that appears on one conductor but not the other, and therefore, "ground loop" -- the introduction of a ground-current signal into a differential mode input (the scope probe).
What does it come from? Inside the generator, maybe their output buffer circuit sucks, and drives voltage into the ground line. Typical construction is a short piece of coax running from the front panel connector to a header on the board (or soldered in), and both ends of that piece of coax are unshielded, so, boom, common mode interference there (even when reading the FG output direct via coax to the scope).
It doesn't help that FG outputs are usually "floating", which usually means, they allow some (SELV level) DC between safety ground and signal ground, but not usually AC (usually being bypassed with a capacitor between grounds). But that bypass is usually done poorly -- a single capacitor at a single point, so there's plenty of opportunity for noise pickup and transmission along the way.
Tim
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