You could look at that situation at negative reinforcement for the behavior of being noisy in the crate. Something "bad" (being in the crate) is removed (she is let out of the crate) when you get the behavior you like (her being quiet in the crate), so she should be more likely to be quiet in the crate in the future (so the behavior is reinforced). However, you could also look at it as positive reinforcement for the behavior of being quiet in the crate. Something good (being let out of the crate) is added when you get the behavior you like (her being quiet), so she is more likely to be quiet in the crate in the future (the behavior is reinforced).
Another example I use a lot is a a kid is throwing a tantrum in the grocery store and his parent buys him a candy bar to shut him up. The candy bar is positive reinforcement for tantrum behavior (kid is more likely to try it again next time because it got him what he wanted), but the stopping of the tantrum is negative reinforcement for the parent's behavior of giving the candy bar (because the kid's tantrum stops when the parent gives him candy). That's part of why it's sometimes difficult to do what you know is the "right" thing to do, because reinforcement/punishment works on everyone and sometimes the "wrong" thing is reinforcing.
Behavior also doesn't always follow the rules. Whether it is reinforcement or punishment depends on the result by definition. Reinforcement increases the behavior, punishment decreases it. That's why yelling at a dog who is jumping and pushing him down can't necessarily be considered positive punishment. For a lot of dogs, it's actually positive reinforcement. You're adding something, but rather than decreasing the behavior (punishment), it often increases it (reinforcement).
At least, that's the way I understand it