Some years ago, they contacted me, too, in the way you describe, but they might not do it anymore.
I booked tickets and paid with my MC, which was not over the limit. Turns out the CC company didn't clear the purchase because I had made too many transactions with Finnair and their system thought there was something wrong
Anyway, the only thing AY did was that they emailed me to inform about failed payment and didn't give any options. I needed to rebook everything and pay with another card. No 24 hour period in which to call in and settle the payment.