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Thanks for the link.
I agree with the comment that for individuals using the keyboard to navigate the box of marching ants is critical and normally I wouldn't eliminate them.
A compromise to to change the border color from white to something that makes the effect look intentional rather than an oversite. The alternate color still needs to be noticeable for those individuals with vision problems.
If someone reading this isn't familar with Section 508 accessiblity issues please Google the term.