Well, you are right. People DO bottle lagers. And they carb.
So have no fear, you CAN cold crash and then bottle. The only consideration would be adjusting the priming sugar to account for the CO2 that very likely already in the beer. Here's why:
When you ferment the yeast create CO2 and alcohol. The CO2 generally bubbles up out of solution, for the most part, at room temperature. But when you cold crash, some of that CO2 remains in solution due to the density of the wort and CO2, just like when you start kegging you will find that a cold keg of beer will accept CO2 into solution at a lower pressure.
So the part you have to calculate is approximately how much less priming sugar you need to ADD TO THE CO2 ALREADY IN THE BEER. I think there's a chart out there somewhere somebody put together. I usually just decrease the priming sugar by a small bit. I've never had a problem with undercarbing, but before I understood about priming when cold crashing, I had a couple of batches that gushed a bit. They can get pretty fizzy!