I'm pretty sure SPECWAR is the only community that still holds an interview with a board of officers from the community. This happens after you submit your preferences, and is considered far more important than your performance in the screener. Screeners are only used to determine who will get the applicable summer training cruise, but it's generally accepted that if you don't do a SEAL cruise your chances are slim to none of getting selected in the fall.
The 'screeners' you hear of are just ways to narrow down the number of interested and give the most qualified the training. Airborne, Air Assault, and Dive schools are the most common screeners. They usually consist of a PFT, ruck run, and in the case of Dive school, a PST and lots of pool time.
The SEAL screener is (rightfully) considered the hardest. Held in November, it's usually getting pretty cold outside. We started at 1600 on Friday and were secured at 2130 Saturday night, with a 20 min nap early Saturday morning. Evolutions include Break-out (3-4 hrs of chaos on HP), 5-6 hrs in the pool, a mile swim in the river, 8 mile ruck-run (mine weighed in at 72 lbs) in under 2 hrs, E and O courses, boat races, a 'base tour' run, and the endless whistle drills, etc. You get the idea. ADM Olson, the current commander of SOCOM came and talked to us as we held our boats at hi-port, and was the one who secured us Saturday night. I shredded two pairs of cammies from so much low crawling on dirt and concrete, but had a great time. There were definitely moments where I didn't think I would make it. My lowest point was during the bay swim, which was right after the ruck run...my legs didn't want to work (water temp was ~58-60), and I recall just looking up at the sky thinking "God...a pizza and a warm shower would be amazing right now"
I wouldn't call it 'politics' but there is some trickiness to getting selected for SEAL or EOD. An '08 grad in my company was thought to have SEALs in the bag, but as his second choice, he put USMC. During his interview, the board of SEALs saw this and commented that he 'really wanted to get into the fight.' He was then told that he would do well in the Marine Corps...
For SEALs, what they're really looking for is someone who's not going to give up on the dream. It's generally known that if you dont' have SEALs as 1st, and SWO as 2nd that you won't get SEAL.