The guy does not know what he's doing. If the hazards work, then the BCM is fine.

Jeezzz. "Auto Electrician", what the hell is an "auto electrician"? Apparently, it's a guy who thinks he knows, but doesnt.
I know that diagram is hard to understand, but it is clear that the flashing function is in the BCM. If the hazards flash, the BCM is FINE.
Did he even use a voltmeter to verify he had power going from the hazard switch to the BCM? If the normally closed side of the Hazard switch fails, you will not have turn signals but you will have hazards.

The other explanation is that the multifunction switch is bad or it's connector is loose. Either would give you hazards but not turn signals.