A great video.
If we go by the rule of buying as much as we can afford, we'd all be shooting for an Agilent 9000x class scope in the $300,000 range. But, once we enter the 33GHz arena, what are we not seeing above it that a faster LeCroy can see at 45GHz? And the list goes on, not to mention the cost of the scopes.
In RF region, subtleties of probe design and placement matter. Where the parasitic oscillations truly there or induced by the act of examining it with a probe, by introducing the probes impedance and capacitance? I don't know. One way to find out is to check the distortion in the collector output waveform, did it improve with the base resistor? or one can double check the base input with an active probe.
So the larger question is, knowing the more you measure the more you see, when do you stop?
I think a more lasting rule is we need to be aware that if we design for X and get X-1 or X+Y, that something is admist and needs to be found, explained or corrected. We shouldn't rely on instruments to find faults by blindingly probing without some conception of how the fault can be formed; so one suspect the faults first and then confirm it with an instrument adequate for what we suspect exists.
Likewise, in complex designs if it does what it was designed to do under the conditions of operation, there is probably nothing more to do, even if there is an unintended oscillation somewhere, because if it is significant it will cause its output to not be the X we intended. So in the example given, if the phase shift oscillator is supposed to produce a low distortion sine wave, which the output clearly wasn't, then it justifies looking for its cause. This simpler rule will last you a lifetime, is not dependent on equipment, and will work on just about anything you work on and will help one choose equipment cost effectively.