Yes....ANY amount of water.....half of a drop....if left to dry will rust the blade. IMMEDIATELY wash and DRY DRY DRY after use....no oil needed. Exception.....salty air environments like coastal areas. I never use any oil on any kitchen carbon blade at all. My wife has been instructed (bless her heart she is a trooper!) how to care for carbon knives. She does a GREAT job. Again, you can use carbon steel (even stuff like O1 that rusts when you look at it wrong) wet all day long...just never let any water dry on it. One single minute with water on some carbon steel will equal rust every time! NOTHING wrong with using food grade oil, tho, AT ALL.
I am amazed how many people have no idea how to care for carbon steel (not directed at anyone here....just experience in selling knives). I just sold two Blue steel knives to a guy who knows his stuff. Or so he told me. When we discussed which steel he wanted, he told me he knew all about caring for carbon steel. OK, I said, and made him two kitchen knives in Blue2. Two weeks later he brings them back to me. One of them had a layer of rust on the blade because his wife let it dry while wet. She said she dried it off, but there is NO way a dry carbon steel kitchen knife will get a layer of rust on it sitting in the kitchen drawer or whatever. Just NO WAY. We live in central Texas, very dry here, not like it's salty air. She just did not dry it off well enough. The other knife, he had cut into a sweet potato. The carbon steel, of course, reacted with the acids in the potato and turned color (patina). He brought the knife back to ask me what that was!!!! Seriously?!?! You told me you knew ALL ABOUT carbon steel!?!? So a little bar keepers friend and metal polish makes them look new again.
When using carbon steel in the kitchen, when you are done using it, THE VERY SECOND YOU ARE DONE USING IT, rinse/wash by hand and dry it off....thoroughly. Store in a block or on a magnetic bar......it won't corrode on you. I recommend using a new carbon steel knife on nothing but meat for the first few months. Why? No real reason other than meat tends to turn the blade a very nice looking blue/purple color. A great base to start a nice patina.
Have fun with it guys!