I may or may not have solved the puzzle. If I did I may or may not have used any of a number of approved and/or frowned upon techniques. In fact, there is a possibility I used a solving program and just copied the answers in.
Now let's spend a day or two getting "ezpz" straightened away.
I don't typically announce how I solve a puzzle. For the record: If I have time on my hands, I always try no green. If I'm more in a hurry, I use greens without hesitation. I often guess on experts (again, that time thing), but solve as far as I can, then try to find the most logical guess (I prefer a 50-50 guess, for example, to a 1/3 guess). AIC is (again, in my opinion) little more than a guess But folks, it's a game.
Difficulty score 23. No green. No red. No wrong guesses.
Tall Mike: expert puzzles usually require looking ahead several steps to eliminate a few possibilities in your approach #1. Easy, Medium and Hard puzzles can be solved by techniques that don't require any looking ahead to eliminate possibilities. Using green helps you keep track of the remaining possibilities.
Approach #2 is basically trying out the possibilities until you find one that works. Of course no one tries ALL the possibilities, we eliminate them as soon as we can to save work.
If in looking ahead to try to eliminate possibilities you stumble on a solution that works you can quit. But if you do, while you have a solution to the puzzle, you don't know if it is the only solution. You are taking that by faith, because legitimate Sudoku puzzle are supposed to only have 1 solution.
If you stick with your approach #1, then you can be sure that if you find a solution that way, it is the 1 and only possible solution to the puzzle.
When I first started announcing I didn't use green to solve a puzzle, it usually meant the puzzle must have been really easy because I wasn't very good at solving them then. Now I usually don't need green. So the no green comments document how my Sudoku solving skills have progressed.
Some people announce Go ... Done, thereby documenting the time it took them to solve the puzzle.
I agree with you drwho that greens help a player to keep track of possibilities, and that many of us use the single solution guarantee as a short-cut. But the guarantee is there, so I personally choose to make use of it. It might be interesting to work on puzzles which may have more than one solution, but I have not discovered a forum for that yet.
Back to the central topic. The more I push my memory the less I need greens. Some experts do not even become a challenge until the end game, and both of the approaches I have described can be implemented without using greens. What I am trying to argue is the total validity of using approach # 2 under those circumstances. It then becomes a somewhat arbitrary personal choice as to whether you look for a solution by small increments or a solution by elimination of impossible outcomes. Either can be done in your head with no greens, reds, side notes, coloring chains, etc. I suspect that other players do this too but wrongly feel that they are guessing if they use approach # 2.
So green, no green; guesses, no guesses; fast or slow; whatever makes this fun for you do it. That's the point, have fun.
Tall Mike: I agree that approach #2 is valid, if you think it is :). Whatever makes the puzzle a challenge to you is fine. The definition of what guessing is is rather subjective. I have a few comments on guessing at my website at the bottom of the page about my solver program. if you are interested.