This attachment shows one page from a statement where I have a $0 balance. If you notice in the "your account messages" section it shows where an upcoming annual fee will be billed. Prior to this statement, there was no spending on this card, thus no statements for several months. I'm guessing this statement was generated to give me notice that the annual fee was coming.

2 months later I received a statement for $99 as expected. This statement also showed the 6,000 annual points to be transferred to Southwest. The next month after that I received another $0 balance statement that served no other purpose other than to show that they had received my payment. For this particular card, these 3 statements have been the only ones I have received in the last 12 months.

If my player 2 accounts were still open, I would also be able to show where $0 statements were given when referral points were awarded. This has been a recurring pattern that is pretty easy for me to notice since these cards are kept open for referrals and there is hardly any spend.