I initially downloaded the image as a png, edited it in Photoshop to change the colour from white to red and then saved it again as a png to place into InDesign. I didn't see any grey fuzz/pixels initially when editing it in Photoshop.
How you changed color may make all the difference in the world. In addition to the original background of the image.
For the sake of clarity, I'll assume the original was a white clipboard icon on a transparent background.
Use the Color Overlay Layer Style
To effectively change the color of such an image, using the Color Overlay Layer Style is best. Why? Because the color overlay will completely cover all pixels on a layer, including any hard to see anti-aliased pixels.
If you were to use the (yuck) Magic Wand Tool to click the clipboard pixels, then merely fill them with red, you will get a slight anti-alias border for the white. Which is what your screen shot is showing. Often these anti-alias pixels can be really hard to see against Photoshop's transparency grid. And the fact that they are white, increases the low visibility of such pixels. Just because you "don't see them" does not mean they aren't there. You have to zoom in, use different backgrounds, or other tricks to force them to be visible at times. Basically, how you changed the color has caused that "border".
There are other methods to change colors which are superior to the "magic wand/fill" method such as channel selections, or layer overlays, etc. But for general icons of a single flat color, the Color Overlay Layer Style is non-destructive and really a breeze to use.