That's not true, you don't have to choose between them. If you use the tv before leaving the room, you can still go do the Social Link afterwards. The only thing that stops you from using the tv is setting up a Sunday date with a classmate.
@Thin_Lizzy: Actually there's two social links you can do on Sundays. The Online Game is likely the easiest one to remember, but there's another. If you speak with Maiko enough at the Nanagaki Shrine, she'll tell you about a guy who visits there on Sundays. Then, talk to him on one of those Sundays and he'll ask if you can find a pen for him. However, the pen can only be found on the first day that Koromaru stays with you in the dorm. Just talk to Koromaru and you'll find the pen. That, simply put, is the Sun social link.
Currently Playing: Resident Evil Survivor 2-Code Veronica (PS2), Persona 3 FES (PS2), Marvel vs. Capcom 2 (PS2), Dragonball Z Budokai 3, Final Fantasy XII