Email from broadband provider about long closed account

Airgas

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Mar 16, 2016
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I recently received a bill reminder (I.e. your bill is now ready - login to your account to view etc) from a (major) broadband provider I left in late 2013. All bills were paid. The email seems to be legitimate, it contains my correct username, and all the links are correct.

I have contacted the provider, who assure me there is no bill to pay and the account is closed. They say 'as our systems are continuously improved, it seems an automated email was generated based on a closed account". They state they have now deleted my email to prevent recurrence.

I was just a bit concerned that this came out of the blue after over 2 years of leaving. Is the explanation they have given me plausible, or should I worry that my data has been compromised? I cannot understand why an auto email would be generated by their systems after such a long interval.