Hey vocax, I had no idea treevet was a saddle salesman. Your buckingham will probably work just fine for you until you decide to try a more advanced saddle. Like said above, thousands of trees are being climbed every day with a simple buttstrap saddle and the majority of us probably started with them.
Crabbing (as treevet called it) can happen. However, it is not a common occurance and there are things you can do to help prevent it. First off, cinch your saddle down tight. I usually wore my buttstrap cinched just below my belt on my jeans. Cinch down the saddle pretty good and the pant's belt will make a bit of a bulge that will help prevent the saddle from sliding up. Secondly, the most common instance where your saddle will slide up is when you are standing either on your hooks or a branch and your lanyard is running from your upper d's around the tree at chest height or higher. You can notice this while standing on the ground. Run your lanyard high around the tree and then lean back in the saddle. You will see a space suddenly appear between the front of your body and the saddle and you can feel your saddle want to climb without you. Take a step up, do a hip shake and pull the saddle down. But fairly easily preventable by not throwing your lanyard too far up. Keep it around the waist area. Also if you spike out, your saddle will want to jump up your body, but this is simply because once again you are putting all your weight on a high lanyard. Even this is not all that hard to get out of if wearing spikes. Once you are actually tied in and sitting in the saddle, I've never seen a crab happen simply because you now have all your weight on the lower d's. Simply remember that a pull upward on the upper d's will lift your saddle so climb in a way that minimizes that.