Wouldn't their lives be like 10X simpler if they just announced they were dating? Sure, the gossip would be around the company in 3 seconds flat, but it wouldn't be very malicious--they're like the perfect power couple, everyone would be squee-ing about it. Then they'd officially have a good reason to swat any bugs coming around, most of the annoying complications would just have to get out of their way--Oh, wait, this is Korean. Never mind.