They don't, and it would be EXTREMELY rare to fix things by replacing multiple resistors,
I agree with that.
However, in the video the guy did measure many resistors which appeared to be high in value.
It would be interesting to know what made them high resistance...
Possibly it is that they are the cheapest crappiest resistors available.
I would expect many resistors to "go high" in an ancient piece of equipment form the 1960s or 1970s, where all the resistors are horrible carbon composition types, but not something made in the last couple of decades.
Even though he measured higher resistance than expected, still resistors can measure in circuit way more than the spec. He doesn't measure them off-circuit.
I would expect a resistor which is in circuit to either read its correct value, or something lower depending on the circuit configuration.
If a resistor reads higher than its normal value it is certainly faulty.
When a resistor in in circuit, it can be in parallel with various other circuit elements.
Connecting a resistor in parallel with another resistor will ALWAYS give a lower combined resistance, NEVER a higher resistance.
So when the guy in the video measured a higher resistance, he could be sure that the resistor he was testing was faulty, there was no need to measure again when the resistor had been removed from the board.
Looking at his soldering technique, he seems to be a believer in the mantra
"The bigger the blob, the better the Job" !!
JimB
An afterthought...
The faulty resistors were not just high in value, but probably open circuit.
Could it he that the mass failure of resistors is due to the metalised ends becoming detached from the resistor bodies due to heat cycling, or physical bending of the circuit board?