Can one be honest but not intellectually honest ?

Julian Sanchez argues that one can, but I am not convinced (click the damn link)

There is a key issue not addressed in this post. If one is making a case (honest but not intellectually honest) does one say that one is making a case ? In a formal debate or a civil case or for the defence in a criminal case, it is clear to everyone that a case is being made and noting facts which undermine that case is strongly forbidden.

To me, making a case in those situations is totally honest in every way. If the best case which can be made without actually lying is p then saying "the best case which can be made without actually lying is p" is intellectually honest.

It seems to me that intellectual dishonesty occurs when someone acts as an advocate but does not say so. When someone states the best case for a claim x without saying "to state the best case for the claim x." It seems to me that this is plain dishonest. If someone claims to be balanced and is an advocate or claims to be just examining the evidence when he is making a case, then he is dishonest.

Or to shrink back a bit and weasel and stuff, I suppose it is possible to make a case without either admitting that one is making a case or actually lying, but I don't think that anyone actually manages to do so. It would require avoiding all phrases of the form "I think", "the relevant facts", "therefore it is reasonable to conclude" and hmm just about everything except for stating selected facts.

I have a challenge. Can anyone find a case of someone who is honest but not intellectually honest ? If someone says "I am going to make the case that X", then does this is totally honest. If someone doesn't implicitly claim to be doing anything else and makes the case, then, according to our host he or she is honest but not intellectually honest. But has this ever happened ?

Has anyone with an audience of normal adults ever managed to slide over the issue of whether they are acting as an advocate without plain ordinary dishonesty. I admit it is theoretically possible (quite possible if one is trying to convince a group of toddlers say) but I don't think it has been done yet.