Why do the points on a refinance depend on my current mortgage?

Looking at refinancing, a salesman is suggesting a double-refinance. The context is that we are looking at a cash-out (to repay a HELOC at a lower rate), and the points are higher for that. The suggestion we have been given is that we should refinance twice (with the requisite waiting period). First to a mid-range rate with a cash-out, then a rate-and-term refinance to get down to the final rate.

As described, the total points paid is a full percent lower than if we did a straight-up rate-and-term refinance. His explanation was that the points are different depending on my current mortgage. To make up numbers, you can pay fewer points refinancing from 5% to 4% and then to 3% than to go from 5% to 3% straight up.

To me, this seems odd, as it suggests that the points I am paying are not based on myself and the current rates, but somehow based on my existing loan. I’m a bit suspicious. He cannot give me concrete numbers because we can’t predict future interest rates, but at the same time, I can’t make sense of why the rules are what they are. Obviously the salesman has a vested interest in the process as that’s twice as many fees/commissions.

Why are the points required to refinance tied to my current loan rate, when that loan will go away once it is refinanced?

Just to add something more concrete. The argument we are being given is that dropping to the lower rate in one jump will cost several thousand dollars in points, but that the same rate can be achieved in two refinances with zero points, and even a little credit.