Excellent point Maribeth, and one that supports my assertion that ASMs should get in the habit of taking blocking.
As an ASM, I have had the responsibility of running full U/S rehearsals myself. While I generally have had access to the PSM's blocking script, invariably, I use my own book. I'm more comfortable with my notations, my shorthand, and know which parts are rough sketches of a scene and which parts are 100% accurate (thus informing when I should glance at an archival video for support).
Along the same lines, on long-running shows, the full SM team is responsible for putting in U/S and replacements throughout the run, and often it is just the SMs, dance captain and a new company member in most rehearsals. As an ASM, yes, you are helping play all those other parts, but (in my experience), it's a team effort, where we all pitch in and help stage "the new guy." I'll notice the cast member is standing in the wrong spot, give the note / question to the PSM or dance captain to confirm, then give the note to the cast member. So that means I'm still "learning" the blocking even after a show has opened, while I'm running the deck, calling the show, etc. since I could ultimately be responsible for relaying that blocking to cast.