This is one of the most uninformed statements that I've ever seen.
1. Piglosi doesn't "own" anything. Congress is a Representative body elected by the people. This isn't a dictatorship. We don't give "ownership" of any elected branch to any one person. We don't give "ownership" of the chamber to any one person. The President has every right to enter that Chamber regardless of Piglosi thinks.
2. The Constitution says that the address is delivered to a JOINT SESSION of Congress. Article II Section 3. "He shall from time to time give to Congress information of the State of the Union and recommend to their Consideration such measures as he shall judge necessary and expedient." So pray tell where does the Senate fit into that picture? Does Senator McConnell "own" the Senate in your asinine world? What do we do with two "owners" who conflict here? I'll answer that for you, your original premise is wrong. Piglosi doesn't "own" squat.
3. What the Constitution doesn't say is WHERE it must be held. If we are following the text, the President can call the Joint Session on the White House lawn if he wants. Piglosi doesn't have a say in this. Tradition indicates that it is held in the chamber of the House, but that isn't a requirement. It's really just for convenience. The House chamber is much larger than the Senate chamber and has more seating. That's why it's held there. Not because the Constitution dictates such.
The Rose Garden would be nice.
Except that the weather in DC at this time of the year is pretty iffy.
Probably wouldn't be good for RBG's "recuperation and recovery", either.