There are a couple six flight reamers. What is significant about the four flight reamer isn't so much that it's four, but, note that it isn't square. Probably designed for minimal chatter, and Frank is likely correct that it is for very fine removal / burnishing.

As you mentioned, flute layout is not even so the cutting is more even, no chatter.

The tool in the original photo appears to be three flutes. could be the photo, perhaps the current owner would weigh in.
Thanks