There's always that worry, but the first deposition is the following day which would give them a single evening to study the material (assuming any video or transcript is immediately available to them) and just wading through it all, never mind crafting strategy around it, would consume about as much time as they have.
Then, even if they do try to come up with a strategy, they can only play as loose with the truth as they assume that BHBH won't be able to immediately call them on it. Trying to dance around a particular point does you no good if the other side has some other piece of evidence that nails you down.
Any time that Casey does spend with these clowns would be better spent getting them to behave or not to say anything stupid that will tank the case. It's like training a puppy. You don't spending time teaching it to do backflips if you're still worried it's going to shit all over the carpet.