In a Dry Heat method (such as smoking) the air around your meat is incredibly, well, dry. This dry air is therefore prone to absorb any moisture it comes in contact with, like the brine. The water is absorbed into the air and the salt remains. This results in a higher concentration of salt and is what is causing your bird to be 'salty'.
If, however, the air is moist already or there is a 'more available' source of moisture (wet method) then the humidity of the air surrounding your meat is already at (or near) it's capacity, that is the air is at it's maximum humidity or it's saturation point. The result is that the already moist air does not draw out the moisture leaving your dish moist and flavorful. In this case the broth will have a more balanced flavor.
Using a brine for a dry method is often a good thing, like a smoked turkey. But the remaining moisture and seasoning will be concentrated through the smoking process and so it requires the right balance of seasoning to get the desired result.
A good example you can look at to compare this is Pastrami vs. Corned Beef. They both start as a brined brisket, but pastrami is either dry roasted or smoked where corned beef is boiled.