Though most players' problem is that of lacking in both confidence and performance, I still hear every now and the from players who are on the precipice of the opposite fate. They are the best players on their teams, and so much better than the others that they feel they may be going too far in being good. What should those players do to make sure not to alienate their teammates or have the teammates hate them for being too good (or appearing as if they feel that they are)?

I'll handle this one, list-style:

Did you earn your position as the best player? Then own it. By this I mean, are you really that much better than everyone else on the team, or were you just that much better one game? Did you really put in the work to be as good as you are, or have you been placed in a leadership position that you didn't earn?
If you did earn your spot, then you have no reason to feel uncomfortable about having it. People only feel uneasy in a position when they know, deep down, that they don't deserve to be there. Sometimes, a lack of confidence can deceive us into belief that we don't deserve spot that we indeed have earned.
If you have put in the work and produced the results that befit your position, then tell yourself that (even out loud, in the mirror if you wish). Every time you tell yourself this (or anything else for that matter -- positive or negative), you reinforce the idea and more firmly set it in your mind.
Any teammates who despise you for being too much better than them shall be given two options: Raise your performance level or get off the damn team. Since you have earned your position, what the hell is their problem? Some people don't like to see another person succeed who has had the same opportunities that the observer had  -- not because they hate you, but because your success is like a mirror being held up to them. If you were able to achieve, why didn't I achieve?
The envy that results can spur someone to either take a hard look at themselves and achieve more, or it can push them to hate you, when what they really hate is what you represent: their own lack of achievement. Armed with this knowledge, don't dim your lights to make them feel better. Shine as bright as you are capable of and that light will either drive them to step up to where you are or run away into the shadows.
Either way, as long as you continue to perform as you know how, you (and your team) win.
The goal of the game is to win. Are you playing to win? Someone may call you a ball hog just because you are scoring the majority of the points -- actually, this is the only time I hear the phrase used at all. Well, dammit, points are how the outcome of the game is determined. Someone has to score them. Just because you scored the most doesn't mean you did something wrong. There's a reason why you're scoring so much, after all. Maybe you are the best scorer. Maybe your teammates just aren't that good. Maybe it's a combination of both.
All basketball players are NOT created equal. Not everyone has the same skills. Just because a teammate is open doesn't mean he or she should get the ball and shoot it. Your 20-foot jumper may be a better bet than a 10-footer by someone else; this is the reality of the game.
All you need to do is ask yourself: Am I playing to win? Are my decisions on the court based on the best outcome for the team or only the best outcome for myself? Do I do what's best for the group or am I only working or serve myself? Whatever it is is obvious to a trained observer. If you can look yourself in the mirror after a game and know you are playing to win, to hell with what anyone else says, teammate or observer.
Consider the angle of anyone who criticizes you. Some people in life will use negativity to bring you down not bivouacs ether negative. It's just so they don't feel so inadequate themselves. There are a lot of people like this in life. Not everyone you meet is a high achiever, and, crazy as it may be to you, and not everyone wants to be.
Human beings are social creatures; we crave connection to others, no matter our level. When you look like you're headed up and away from from your current peers, they will try their hardest to keep you down there with them -- even though it would be just as easy for them to rise with you. It's not something that I can completely explain, and you don't even need to completely understand it. Just know, observe and accept it. People aren't going to be shit but who they are. Let them be that. You are only responsible for you.