The Smartypants Waitress

Another old paradox/riddle (that baffles some and others easily see through):

Six friends make reservations for dinner at their favorite restaurant, but on the way there they run into another old friend, who then joins them. When they arrive at the restaurant the waitress says she only has a table for six available, per the reservation, but then thinks for a moment, and says 'don't worry I'll work it all out.'
She then proceeds to seat person #1 in the first chair and asks the second person (person #1's girlfriend) to sit on the first person's lap for the time being. Then the waitress proceeds to seat person #3 in the second chair, person #4 in the third chair, person #5 in the fourth chair, and person #6 in the fifth chair. At that point, looking very self-satisfied, the waitress tells the lap-sitting girlfriend to go ahead and take the empty 6th chair, and WAA-LAAAH she has successfully seated the whole party! ...or, NOT!!??