The difference between TNG's setup and TOS' is that the dilithium crystal matrix is separate from the M/ARC during TOS, while during TNG, the dilithium crystals are held right there in the intermix chamber itself.
Remember, the whole purpose of the crystals is to amplify the energy from the antimatter reaction so that a decent warp field can be generated. So, as long as the warp drive isn't engaged, then there's no problem popping the crystals out to take a look at them. If Geordi tried that on the Enterprise-D, yeah, you'd have a very big problem, but on the original Enterprise, the intermix chamber is a couple of decks down. Still wouldn't be a smart move on Scotty's part to pull those crystals out while the ship was at warp, but not necessarily the instant death for all aboard that's being put forward.