South African Airlines has the same policy. If you book through a online TA like Expedia.ca, you don't have to worry. It can be a hassle, but they do clearly state this in the booking process and the confirmation e-mail.

However, I think I had the same thing happen once, and was able to pull up an old online statement on my computer with the old number... Did you try calling AMEX on the spot so they could confirm to SQ that the AMEX you have replaced the old one?