Thank you! I have sent. I hope this is what you requested.
OK. The document is set up as a single-sided document, and there's only one "section" in it. That lets us know that the document doesn't have any artificial page number changes.
Let's try this:
Go to the File>Document Setup... menu command, and when the dialog box appears, select the Facing Pages check box. Then check the Pages panel again. Hopefully it stacks up like the example at right. Then try to print it again, and see if it gets the same result or a better one for you.
Sometimes a print driver is finicky about how it defines a duplex printing job. It could be that since your InDesign document isn't "recognized" as a two-sided document, the printer driver isn't seeing it that way when you output it. I've seen this happen before.
And as for the question you asked above, why would you have to go through the extra step of using a PDF, it was because that also could get you past your problem. That's all we're trying, and able to do.
Both of these are worth a try to get you past your problem. Whatever works, right?
Hope this helps,
Randy