I've always thought that precision and concision went together rather well. In this post, the author implies that more words bring more clarity. Now obviously, an extremely terse utterance can be vague or ambiguous, but I don't think concision itself is inherently vague. Concise writing is writing high in information. It is not necessarily brief, since a concise history of the world would still be 2,000 pages. The word "terse" implies that necessary information is withheld, whereas the word "concise" implies that the writer did not use unnecessary words.
Redundancy in writing can serve the purpose of disambiguation. Suppose we are meeting on Friday at 8. Well, we might want to say Friday, Aug. 26, at 8:00 p.m. Where are we meeting? Starbucks. But which exact Starbucks? Friday, Aug. 26 is redundant, because August 26 is a Friday, but more information allows for less error. If someone said Thursday, Aug. 26 we would have to clarify. Do you really mean Aug. 25? Careful writing, though, can still be high in information per word without using too many words. Really verbose writing forces the reader to find the main points amidst the verbiage. Writing low in information tends to make me skim over large passages very quickly. I often have to go back to find out what the point was.