According to the article, the machine reads a special ink from the lids of the cups. My assumption is that the orange dot on this clip contains that ink so as to fool the machine, not just block the reader.

Fair enough, cover it with a discarded cup+tape?

That's what these guys [1] did.

[1] http://www.keurighack.com/

There's a special ink on the cups that the brewer can detect - I can't remember the specifics.