I don't know a single person that either has KSM or AOTC that doesn't have 4 piece. That is 3 piece right off the bat. Not saying it's impossible but chalk that up to incredibly bad luck if you have full cleared the raid on all non mythic difficulties and not gotten a single piece of tier from either your vault or a drop.
This more likely sounds like a situation of bad planning if it actually happens- spending your AOTC/KSM omni token before knowing which piece you need or likewise for using catalyst charges.