Well now Rapaire, the way folks 'round here would work that deal is that the lodging was compensation so was taxable, but the fact that he worked on this trip made the whole trip deductible as a business expense. So of course the lodging that he paid for by working was a direct offset of what he received - i.e. no tax; but by performing "compensable work" he made the whole trip a write-off.
Had he reported everything properly, he probably could have gotten a deduction for his transportation to (and maybe back from) Alaska as "business expenses" and maybe wiped out all of his taxes for the year. (I hear it's very expensive going to Alaska - if you want it to be.)