A proper brine mixture will not make the butt/shoulder taste like ham, and it is not too salty (if it is salty that could be the reason for the hammy taste). I also agree that for the most part meat is brined to keep it moist during cooking. As stated above the shoulder has enough fat to keep it moist, especially if you hold it in a cooler for a couple hours. However there are brine recipes designed to add flavor into the meat, more-so than just to keep it moist.
I used to brine pork, and had good results with great flavor. Then I started injecting which made the task easier and less clean up. I used Chris Lilly's Injection but found it to be salty to my tastes, I cut back to almost half the amount of salt and it was very good. Last year I switched to OakRidge Game Changer Brine as my Injection and have nothing less than great results with it.
I now, always use OakRidge Game Changer Brine as an injection. I Use fruit juice (Peach, Pear, Apple, or White Grape) for added flavors. For every 8 ounces of juice add 1 Tablespoon of OakRidge Game Changer Brine and then inject into the pork. I inject right through the cyro-packaging to save with cleanup, using different angles through the same hole to prevent leaking. I used to rub and let the pork sit overnight, but now I'll rub a few hours before smoking depending upon my time constraints.
When cooking injected pork butts I find the bone begins to wiggle at about 187°, I pull and rest the pork in a cambro/cooler for 3 to 4 hours, and pull the pork just before serving. I find the OakRidge Game Changer Brine keeps the pork exceptionally tender, moist, flavorful, and it pulls in very long strands which is great for sandwiches.