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I'd feel comfortable in taking their word for it. This offer seems to pretty much always exist with them.
They always extend the BT offers. I have had my Promise for almost a year and a half and it has been continuously extended. So yes it's true.
In regards to making a payment and reflecting towards your available credit, new members must wait I think 120 days or so for your available credit line to reflect the payment. In the meantime it will always take 10 days for it to reflect. Same goes with cash advances.
I could be off a few days on the wait time. But it's at least 90 days.
In my experience with them they extend the BT every 3 months. It's wonderful!