You wouldn't begrudge a player taking a look at the table from different angles before taking an action or setting his dial. You also wouldn't take issue with a player asking for the damage total or ability wording on a ship of yours. Or calling a judge to get a ruling before making a move.
None of those things are "playing the game" as you put it, but they are accessing available information to inform the plays about to be made. Looking through a damage deck is no different. It's available information that in some instances is relevant to helping decide what to do, just like checking angles.
Now just because a player has information avaliable to them and has the ability to utilize it, doesn't mean they have an absolute ability to do so. At some point you cross the line into stalling.
Moreover all those things you describe as playing the game, you can be stalling while doing those to.
You came around to my point when you brought up stalling. All of the previous items you mention help advance the game - checking angles helps you decide on a maneuver. Asking for damage totals takes only a second and helps you decide what attacks to make. Checking a ruling assures something is legal.
All of those things are information made available, but all are moving the game forward (at least as long as they are not used excessively to stall). How does reading the discarded cards in the discard pile help advance the game? It lets you guess what might be up, but again, how does that help move the game forward? I understand that it's legal and as long as it's not abused then whatever, but I don't see how it could help in a timed game.