It is a local printer problem; your being able to print it out correctly shows so.
It is not related to overprinting. Something went wrong in the printers’ RIP software (the program that creates a super-high resolution bitmap of your PDF) while decompressing that particular CMYK image. The usual sequence of “Cyan,Magenta,Yellow,Black” pixels got messed up, and then all went out of sync: the values ended up showing the wrong colors, and parts of your image moved around.
With the right software, your printer can try to apply another kind of compression on this one image, straight inside your PDF. You can also help (a bit): check what image conversion settings the PDF export uses under “Compression”. If it’s “JPEG”, change to “ZIP”; if it says “ZIP” then change it to JPEG and set the quality to “Maximum”.
You don’t have to do anything to your original image! When exporting to PDF, InDesign is going to convert and store your image as it says in the Export dialog, regardless of how you saved it from Photoshop.
Export just this one page — if your printers’ software is not up to specs, flaky, or otherwise contains Bugs of the Unexpected Kind, you might ‘destroy’ other images that were printed correctly before.