Earlier quoted context omitted.
The rule is to use the same pronoun you'd use as if you didn't have two parties involved, right? "My friends and I did X" is right because "I did X" is, and "Me and my friends did X" is wrong because "Me did X" is obviously wrong.
Sorry guys, not a native here. I am sorry if I upset you with my poor English. I learnt my lesson :)
I suspect if you aren't a native, the reason you say "my friends and me" is because it's a bad habit you've picked up from natives, like typing "gonna". I think anyone who can make a sentence such as,
"We cleaned up the procedure names manually, and matched the procedure related specialties to the hospital specialty ranking made by US News, and it gives much better perspective to the users"
is far beyond making English 101 mistakes confusing objects and subjects of sentences. Actually, in 15 years of on and off English teaching, I have run into very few non-natives who have that issue, since they had to actually study it. I find you to be somewhat unique.
In any case, there are plenty of natives who consistently say write and say this, so hopefully a few of them will take it to heart.