Dunno if this is of any interest but I did a quick video showing the trace noise/wobble on my old scope when there is an intentionally generated 30dB S/N ratio on the test signal caused by wideband noise.
I scaled it down to 10MHz so to get a 30dB S/N ratio I needed -101dBc/Hz of noise in a 12.5MHz BW.
I produced this noise using a wideband noise source and a step attenuator, a 6dB splitter/combiner and a 12.5MHz LPF. The metal box with all the holes in it is a wideband high level noise source.
12.5MHz BW is 12.5e6 bigger than 1Hz. The marker shows -101dBm/Hz power in a 1Hz BW so the power in that 12.5MHz pedestal is 12.5e6 times bigger.
So the power in the 12.5MHz BW is 10*log(12.5e6) bigger or 71dB bigger.
-101 + 71 = -30dB so the S/N ratio is 30dB. I also checked the S/N ratio using a 20MHz Racal true rms meter and it was close to 30dB.
You can see the noise pedestal on the analyser and then the scope shows how much wobble you see with a 30dB S/N ratio.
I briefly increased the noise to a 20dB S/N ratio on the scope and that causes the brief burst of very bad wobble at 1:02.
Sorry about that, I turned the attenuator the wrong way briefly.
But you see the wobble diminish on the scope when I increase the attenuation to improve the S/N ratio to >= 40dB.
In the last few seconds of the video you can see me swapping back and forth between 40dB and 30dB S/N ratio and the wobble can be seen to almost vanish at the >= 40dB S/N ratio.
If I had done this at 100MHz with a 125MHz BW the wideband noise would need to be at -111dBc/Hz to give this amount of wobble.
If I had done this at 1000MHz with a 1250MHz BW the wideband noise would need to be at -121dBc/Hz.
If I had done this at 3000MHz with a 3750MHz BW the wideband noise would need to be at -126dBc/Hz.
A sig gen set to 3GHz is unlikely to be this noisy unless it was faulty but the scope system noise might be quite high so it might be possible that the cause of the wobble on the Tek scope may be partly due to wideband noise. But it's more likely to be something else IMO.
The video is just a quick and dirty demo so sorry it is so basic and brief...
https://www.youtube.com/watch?v=0vCgQtGJMno&feature=youtu.be