Ah, I was told two week ago by my supervisor that my work style was annoying everyone in my department - my supervisor told me to "slow down". Seems to she kinda' threw me under the bus to everyone else also. It seems my willingness to jump in and just get things done is perceived by others as taking over and I guess I inadvertently stepped on some toes. When I finally brought it up to our department head he told me not to worry about it that he thought my work style was fine. But, gad, it makes for some awkwardness at the office. Ugh.
Seems like you co-workers are on the defensive and instead of just stepping up they would prefer to try and lay all the blame on you for their errors. I think the email route is the way to go. Email is tone neutral and creates a paper trail for you. Which you may need if those 2 keep running to the bosses with every little perceived offense. Also, carbon copy your boss on the emails, let him know that you are doing that and tell him to critique your tone as you want to "ensure that the message is professional". Yeah, a little bit of suck up there, but with two of them batting for you, you may need to be a little like that for awhile.
It is really hard to spend your days watching every little thing you say and how you say it. But it does sound, especially from your SWH, that they are just on the defensive and it would not matter how you corrected their errors, they would be upset about it.
Good Luck