The interesting point is that this video demonstrates the benefits of a "precision" cooling design. The Filter instrument doesn't really has a precision cooling design. So, lid on or lid off, the bulk of the cooling is driven by local convection.
Yes, the fan removes that heated hot air from inside the box when the lid is on, but the mean velocity over the individual heat sinks (even those close to the fan) is too low to significantly boost the performance (degC/W) of those sinks via forced convection. (This is because forced convection really only starts to occur when local flow in the heat sinks boundary layer becomes turbulent. i,e, that largely static boundary air is broken down by high velocity air moving and swirling around it).
So in that case, the heat sink temps don't change too much between having the lid on or off (when the lid if off, the lower density hot air natually rises away, pulling cold air into it's place).
In the case of the filter instrument, the fan really is there to ensure the bulk temperature inside the device stays within a few degrees of ambient, NOT to ensure any particular component of sink is cooled! (This is important for instruments that may be mounted in racks (where they get upheat from their neighbours) and/or used in higher ambient temperatures etc)
For the 'scope, the individual ICs that are rejecting heat don't have a good sink (high thermal impedance), so they require the fan to be blowing high velocity air. This is getting closer to a precision cooling design, where you need to have the covers on (or cling film instead) to ensure the air paths impinge on the correct location. Without that turbulent air flowing over the specific ICs the device overheats.
We of course see proper precision cooling in devices like DC loads, Power supplies or modern PC's laptops etc, where specific and direct airflow is used to ensure sufficient heat is removed directly from the device being cooled, and not just allowed to spread into the general internals of the device. In those cases, fans directly on heat sinks, or moulded channelling etc (or even heat pipes etc) are used.
It's also worth noting that with IR measurement "emissivity" is everything. Generally, the camera will be set for a fixed value (usually a "black body" value. So, for accurate measurements you either need to correct the camera settings for the objects you are pointing it at, or another common option is to just lightly spray the entire pcb with black spray paint!!