There really <i>is</i> a gray area between "home" and "public exhibition" and it is extensively litigated over.<p>It sounds like a simple, reasonable thing to determine. Something that would never ensnare honest people who inadvertently walked across a line you imagine is well-delineated.  But it really isn't.<p>Are most personal parties in the clear, despite size of  TV? Sure. 
Does that mean all of them are or that you'll clearly <i>know</i> when you cross that line?  Case law says "no" on both counts.