I've seen гласность translated both ways and seen the English translation debated. I've read it's from a root word meaning "voice" or "tone of voice" ("voice: с. голос, глас. . .":
voice: Babylon English-Russian), which I'd infer is where the "publicity" definition comes from. I'd need to find a good Russian-English dictionary to say much beyond that. Most online dictionaries (at least ones I'm finding from searching in English) don't seem to get deep enough into the etymology and entries to answer the question decisively.