A lot of domestic cats have some Persian somewhere in their ancestry, as Persians have been around for a very long time. Depending on where you live, there may be a statistically greater chance of Persian ancestry than Maine Coon, simply because there were more of them around.
While modern Persians have a very distinct head, if you look at very old pictures of show champions, they don't look a lot different to the picture on page one of this thread. So, I'm going to go with "Persian mix" as a very likely possibility. It might be many generations back, but as long as both parents were carrying that recessive longhair gene, it will come out.