Spring League game last nite. 3 person crew, I am C. Team A down 2 shooting 2. Missed the first. Intentionally misses the second by launching the ball at the rim, hits the under side and deflects. Trail blows the whistle and signals that the ball never hit the rim. When the whistle blew no team had possession. We huddle up to make our decision. I saw the ball hit the rim, and the Lead saw the ball hit the rim. My suggestion was to go to the arrow since it was an inadvertant whistle w/possession. My two partners, with much more experience over ruled me and gave him the free throw again. At the end of the game we discussed the situation again, and realized they had made a mistake.
HOWEVER, at the beginning of the game as I was getting ready for the toss I made sure the players were facing the right way. (One team only had five the other six) I looked at the benches to double check and sure enough a white jersey was sitting opposite of basket. A few trips down the court Mr. "White Jersey" has flipped it over to the blue side, thus we are going the wrong way. There were no organized warm -ups so it was hard to judge until game started. We finished the game going the "wrong way". Not sure if I should have switched at some point.

Whatever made them want to do that?

Cute story, I think there should be a "Doh!" in there somewhere. :) I wouldn't have switched them, no biggie.

Yes, your partners goofed the free throw. A good pre-game helps with the T and C getting this call correct. The L shouldn't be looking there at all. Since the whistle was sounded without possession, you should have used the arrow.

In the second situation, the rule is that when the official recognizes that the teams are going the wrong direction they switch them and all points scored, fouls committed, and time consumed stand (4.5.4). However, since you said this game was only lightly organized, like Dan said, it is not a big deal and you probably don't need to switch them. It is probably easier just to ask the one sub to sit on the other bench!