Sorry about the title but I'm not quite sure how to word it.
Hopefully this will help explain it more:
For your case in indesign, just expand your frame and the flat parts will be gone, the resampling causes the circle edges anti-aliasing to extend outside of the default bounding box.
Working for a company with a circular O in the logo, I've had to deal with the downsampling issue quite a bit. The 'flat tire' is an issue that frequently occurs when others try to use our logo and try to resize it.
Prior to Photoshop CC (where you are working with instances of files) when dropping in an .EPS, then free transform scaling it after it was rasterized, almost every time it would flat-tire. The way to avoid it was to import the EPS at the exact final size you needed it into your PS document. I found myself guessing the dimensions and re-importing the EPS many times over as a workaround to keep the 'tire' pumped up.
Unfortunately Adobe hasn't yet discovered the secret to resampling a smooth circle when resizing it...
I am experiencing this exact problem right now! If it is true Adobe hasn't found a way of exporting nice circular edged graphics from InDesign, I am pretty dissapointed...
I have found a workaround that's worked for me though:
I have to use these PNGs in InDesign coz they're external graphics I've received, and would be too time-consuming to try recreate them in illustrator...However as the only part I'm having trouble with is the circular edge, I thought why don't I just trace over the edge in Illustrator?
I tested it, and it worked. I just made sure to make the stroke width thick enough to completely cover the edge, then dragged both the PNG and the illustrated vector circle into InDesign.
It exports fine as a PDF now, and even when zoomed in on, the vector edge maintains its crispness.