Image has Bad Down Sample out of InDesign

Hopefully I can make this make sense, it's a bit convoluted. We're using client-provided files, and they made the poor decision to create a likeness of graph paper as an image instead of vector.

This image was placed at 17% reduction in InDesign and exported to PDF just fine using the client-provided setting that bicubically downsamples to 350 if over 525. That page with the graph paper was then extracted from the PDF produced by InDesign and placed in ANOTHER InDesign file as a thumbnail at just 18% of that 8.5 x 11 page size, now a major reduction from the original file size for the graph paper image.

Using the same export settings out of InDesign (bicubic to 350) the graph paper in the thumbnail comes out like this:

We first thought that might make perfecet sense given we're taking that placed PDF page with that tiny graph paper image, which is now approximately 2054 dpi effective resolution in InDesign, and down sampling it to 350 dpi.

But, if we do a similar reduction to that graph paper image neither Photoshop nor Acrobat seems to break it apart as much as InDesign. The example below was exported from InDesign at FULL resolution with the resulting PDF then Save as optimzed from Acrobat using Bicubic downsample to just 200 dpi (150 dpi LOWER than InD) and isn't nearly as broken up as the 350 dpi coming out of InDesign.

We're tried all the different down sampling methods well as the different compression methods out of InDeisgn but can't figure out why InDesign is doing what it's doing to the lower res image.

Thanks for any insight you can offer,

Ken