Well, there is a big difference between not paying for 60 days (which is significantly delinquent, reported to credit agencies, possibly at risk of account closure and being sent to an external collection agency, etc) and missing a payment by 1-2 days. Remember that until it's 30 days late it's purely an internal matter -- it doesn't even show up on your credit report.

Amex will also take your entire point balance if your account is closed so there's no difference there (I keep an everyday card that I rarely use just to keep my MR points alive)