You might say the first angler must have been doing something wrong. Not necessarily so say I, grilse can move through beats very quickly. Often it's not long after a shoal of fish is seen entering a pool that one is caught. It's a gamble. If the pool I'm fishing is a good one I normally give it another chance, should nothing happen I would have no hesitation in moving upstream to try to intercept the running fish again if possible.
Small rivers are a different kettle of fish.
When they are low, virtually nothing goes far past the sea pools. Given a spate at the right time however it's a completely different matter and the river should fill with them. Fly-fishing at grilse time produces something of a dilemma for the salmon angler. Much depends on the size of river you have to cover and what you expect to catch. On small rivers this is not too much of a problem.