Through-checking your luggage doesn't necessarily connect the check ins together. The baggage tag system is independent of the check in.

A good check-in agent will try to check you in remotely so that the baggage information can be connected to the next check-in, but the bag can be tagged for the flight without that happening. That's when you need to take the baggage receipt to an agent of the subsequent carrier to get the records linked together. (If you do this across PNRs it's a good idea to do this anyway!)

Obviously, for security reasons, the bag will not be loaded if the passenger is not checked in (or if the records are missing); and the bag will be unloaded if the passenger doesn't board.

If the bag is already loaded the airline will have to spend time finding it in the hold so that may persuade them to wait a few extra minutes for you. A bag turning up unexpectedly for loading may also force them to figure out what is going on and who it belongs to.

Either way I think the guy is answering a different question.

You can ask the airline to link your PNRs so that the next agent can see that you did come from another flight that was late. It may also be investigated by the gate staff as the flight closes. But it doesn't guarantee anything.