I made up a fake problem with our apartment to get my roommate to stop singing in the shower, and now half the building believes it

My roommate loves singing in the shower. Not humming. Full-volume performances at 6:30 in the morning. Same four songs, every weekday. A few months ago I was exhausted and told him, completely off the top of my head, that the bathroom vents in our building are connected vertically and everyone above and below us can probably hear him. I have no idea if that's actually true. He looked horrified and immediately stopped. Problem solved. Except a week later I heard him warning our downstairs neighbor about the "weird vent thing" because she mentioned doing karaoke at home. Then she apparently told someone else. Last month a guy from two floors up was in the elevator talking about how sound travels through the bathroom ventilation in this building and how "management really should fix it." I said nothing. Yesterday our landlord emailed everyone reminding tenants to be considerate about noise because he'd received several questions about the bathroom ventilation. There is now an actual building-wide rumor based entirely on a lie I invented before coffee because I couldn't listen to Mr. Brightside one more fucking time. My roommate even told me this morning, "See? I told you that vent thing was real." I agreed with him.