[jcranmer]

To be frank, this is an issue where there's an abuse of terminology going on, although the people asking the question probably don't realize there's an abuse of terminology.

"Is X computable?" is asking if there is a program that is capable of printing X out. For any integer, the answer to this question is trivially yes.

But when people are asking "Is BB(6) computable?", that's not really what they're intending to ask. What they're trying to ask is "is it possible for us to figure out what the value of BB(6) is?" In a more precise sense, the question is "Can we prove {BB(6) = x} is a true statement for some value of x?"

To some degree, I think Scott is being somewhat specious here. The question may be somewhat malformed as written, but it's also pretty clear to an expert what the question meant to ask, and--especially when you're targeting a more lay audience--insisting on giving the trivial answer to the clearly unintended question isn't likely to help the situation much.