One 30-day late payment on your credit report can drop your score significantly. For example, if you had a reasonably respectable score of say 700, your score might have dropped to as low as 620 from just that one late payment on your credit report. That's why it's so important to make payments on time.
Regarding your question about payment insurance: The answer is no. Your credit score isn't affected by the source of payment. It could come from you, your insurer or your Aunt Tilly. All that matters is that the payments are being made on time and as agreed.
From my experience with credit card insurance, you are lucky that your claim is being paid. Several of the big banks have been sued and paid out multimillion dollar settlements in connection with how their payment protection plans were run. Many of the large banks have dropped their plans as a result.
I generally discourage people from credit card payment insurance. It makes more sense to me to put cash in an emergency fund, and you can dip into that fund when you need to. Also, you should consider building your own repayment plan using Bankrate's credit card payoff calculator.
Now, a word about your 575 credit score. A 575 score suggests that you have other issues on your credit report besides a 30-day late payment. Either way, it should take approximately two years to see your score improve to what it was before the recent negative items on your credit report. You have already done the essential step to begin recovering from your late payment by catching up on the payment and continuing to make on-time payments. Should you have any other accounts where you missed a payment, be sure to take care of them as quickly as possible. If not, you'll have a string of 30-day late entries on your credit report.