I was thinking the same thing, but the beginning of the following step (#4) cleared it up for me.
This example is trying to look at how (in)adequate future premium revenue would be without any rate changes, compared to “projected claims” (i.e. projected claims rate applied to projected membership). They are calculating the “projected premium” as projected membership applied to current premium rates, rather than using a projected premium rate, which I think is what we were both originally thinking. They then compare the projected loss ratio, using these two pieces, to the target loss ratio in order to estimate the needed rate increase.
So your formula is assuming they would change rates, but they want to keep rates unchanged.