Although I strongly agree with the answers given so far — no racial overtones to renege — you must bear in mind that the kind of people who frequent this site are linguistically aware and, therefore, not necessarily reflective of your supervisor or your work environment.
What you’ve stumbled across in your supervisor is the “eggcorn” phenomenon, where speakers who are (partially) ignorant of some word give it a false etymology that accords with their (partial) understanding of its meaning. (For instance, acorn sounds like it’s made up of corn and a. But what’s an a? In dialects where egg rhymes with vague, it’s easy to reinterpret this as the (eponymous) compound eggcorn, as acorns are vaguely egg-shaped.)
In the case of renege, I bet your supervisor thought, “It means something negative, so it must be related to the racist derivatives of negro.” (As you correctly point out, the same thing has happened to niggardly, which is as stigmatized by some speakers as the derivatives of negro are.)
As a linguistic process, though, the phenomenon is ancient. The word bridegroom is a case in point. Historically, it ought to be bridegoom: the goom, ‘man’ (cognate with the hum part of human), of the bride. But, when English eventually lost the Anglosaxon root guma, bridegoom ceased to make intuitive sense to English speakers and was replaced by the current, somewhat bizarre compound suggesting that women marry stablehands.
Eggcorn etymologies of the sort you’ve encountered occur at the phrasal or idiomatic level too. Black magic (as opposed to white magic) and dark day are felt by some to have racist overtones or implications (Ossie Davis famously makes this case in “The English language is my enemy”, for instance) — though advocates of this view generally (universally?) ignore the fact that black and white have the same metaphorical extensions (bad versus good) in traditional Igbo and Luganda proverbs. An op ed in the The New York Times (from 1988) consequently urges prudence, or self-censorship, here.
So, though you are right, you should be aware of people’s propensity towards misconceptions in this domain.