I don't think I'd allow a player to just say "I'm rolling survival" and not tell me what they are trying to achieve with that roll (presumably in the hopes of catching me offguard). In fact, I think that leans more towards a gaming the game mindset. The rolls are there to facilitate what you're trying to do, not the drive it. I know that you can play RP games anyway you want, but in my mind I feel like the beauty of pen and paper over video games is it's not discrete actions - the entire premise is "this is the setting, this is happening, what do you do?" whether that is dialogue, or an action, or combat, or whatever -and then the rolls just help resolve that - they come afterwards.
EDIT: I know this wasn't really on topic with Friartook's specific issues - I was more just speaking generally based on some comments from that. Also, I'm not quite sure I'm correctly interpreting "the players make the skill check call".
This absolutely on topic for this discussion! You make a couple very salient points in your second paragraph: "The rolls are there to facilitate what you're trying to do, not the drive it." and "in my mind I feel like the beauty of pen and paper over video games is it's not discrete actions". Rolls are more or less meant to represent abilities the PCs are good at (whether the players are or not) and the influence of random chance on a situation.
Let me give you a couple very real examples of what I've been dealing with:
PCs enter a warehouse. I describe the warehouse, its inhabitants, and the layout of the room noting many relevant features. One of my players says he wants to do a perception check ("the players make the skill check call") to get more detail on the security situation. In this case, I'm ok with that check, he rolls really well, I give him a bunch of extra detail and even allow him to make a computers check to get an idea of the electronic security in the room. Relevant exposition abounds; player tries to push it and gain even more, I say no, that's all you can get out of your stellar roll.
We move on, some stuff happens. About 10 minutes alter another players says he wants to do a perception check on the
same room. I say, "...ok...what are trying to figure out with this check?" Player says, "I want to know the layout of the room and how many guys there are guarding it." I say, "That is information I've already given and you don't need to roll for it. What you're really saying is, 'I wasn't paying attention when you described the room, can you run it by me again?' No problem, I can do that."
Another example (the metagaming example I called out earlier):
One player is engaged in a game of cards and gambling with two NPCs. His buddy decides he wants to take a back-up position. I say, "Sure, they've given you free run of the warehouse, you can take a walk." He calls for a stealth check to make his way onto the overhead catwalk. This area is totally exposed and in order to get there he has to walk across the open floor of the warehouse (in plain view of at least 6 guards) and has to pass two guards to go up the stairs to the catwalk.
I say, "There's no real need to sneak, and you really can't sneak through these guys, they are actively watching you. What are you trying to accomplish with this sneak check?"
PC: "I want to make my way to a good position on the catwalk where I can get a shot off at the guys gambling. I want to be in a good position to back up my friend."
Me: "Fair enough. In the context of that, what are you trying to accomplish with this sneak check?"
PC: "I just want to make it so I'm in a good position. I want to be prepared in case the game goes south."
Me: "Ok, so again, in the context of this scenario, where does your sneak check come in?"
PC: "I just want to make it up there sneakily."
Me: "So, you want to go up there, and not have these guys see you in position? That's going to be really hard."
PC: "Yeah, that's what I want to do."
So, a sneak check gets rolled, he is successful, with several advantages and a despair. As the despair, I have another NPC come out, one who actively dislikes the party, and mean mug him. So the other guards didn't really take notice of him, but this guy did.
He says, "Ok, but as my success, they don't know why I'm up here. They don't realize I'm trying to back up my buddy."
Me: "Wait, that's what you're trying to accomplish? That's what I was trying to get out of you. That's not really a sneak check, that would be cool or deception, but not sneak."
PC: "I know, but my sneak is better."
*sound of squealing brakes as I pull the emergency stop on the session*
That is what I am dealing with and that is why I have instituted the policy that players may never ask for a skill check. Instead, they must tell me what they are doing, I make the initial call, and we can discuss. I don't want my players thinking about what skills their sheet says they're good at, and trying to game the game (and me) like that. I want them thinking about the narrative of the situation and what actions they would take as their character within that narrative. One is thinking about the game mechanics, the other is thinking about the game world.