Both true. I would have gotten the bit about emitter followers being able to oscillate, because while they have no voltage gain, they do have power gain, so can be made to oscillate nicely with a multi-tapped ferrite pot core inductor and a film capacitor. This is how the old Touch-Tone keypads worked, with Germanium transistors even. Later were silicon.
My equivalent to your emitter follower test is higher-level, because I was in the software labs in those days, but we were interfacing to hardware.
I would give the candidate a 11x17 inch sheet of paper and a pencil, and ask the candidate to draw a diagram of the components of their senior project, and walk me through it step by step. This was quite effective at eliminating the poseurs, as they could not get much beyond high-level platitudes. People who had actually designed a built something would not run out of deep details.
And I was on the receiving end of such a question when I was job seeking in the 1970s or so. There was this startup which was building something that ran on SEL 32/55 midi computers, an IBM 360 clone optimized for process control. (SEL 32/55s are now a chip.)
The question was to diagram and explain how an I/O Channel Control worked. It's a linked chain of data blocks, each block specifying an action or setting. In those days, these blocks were data structured usually generated with macros, but in earlier days one just wrote the data structure directly in hex.
Anyway I passed, but the company was a bit too anarchic for my taste. Many years later, my main interviewer applied for a job (not knowing that I was the manager), and I hired him. The very fact that he could follow what I was saying back in the day was enough proof of capability. Small world.
Joe Gwinn