For people in a hurry: I've just installed a new keyboard, and didn't bother to glue the rivets. Yes, the keyboard doesn't feel as springy as it used to. Does it work? Also yes. This shouldn't have been designed this way, but it also shouldn't stop you from repairing it anyway. A scalpel works fine to sever the rivets. Make sure to wiggle the knife and steady your hands so you don't cut any cables accidentally.
Interestingly, there seemed to be some kind of short in the original keyboard: part of the plastic was molten. The "n", "b" and spacebar keys weren't functioning on this unit. I left out the keyboard backlight in the repair, because I suspect that was the cause (keyboards themselves don't carry enough current to create molten plastic like this).
Could've been a fire, Lenovo....
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