Chelsea could have got 2 penalties. Are they clear penalties ? No. Do you often see penalties given for similar facts: yes, very often.
Barnes on Ivanovic is Always a red card on the continent: he never had the intention to play the ball, didn't even look at the ball. But, maybe Englis people and refs see this as a yellow. I hope something similarly will happen against a City player, i wonder what your opinion will be then. Might be that you still think it's a yellow. You certainly are not an unfair guy.
Where you are completely wrong is about Barnes on Matci. The fact that it's accidental is totally irrelevant. Witsel's horror tackle on Wasilewski was accidentally (young Witsel was horrified by Wasilewski who was the most dirty player in our competition). Was it a justifiedred ? Yes, it was.
Did the Birmingham defender had the intention to break Eduardo's leg in the match against Arsenal. I don't think so. Was it a justified red ? Of course it was. What Barnes did on Matic (and IMO on Ivanovic and before that on another Chelsea player, i don't remember which one) is always a red card.
Like i said in the referee thread: referees should protect players. What Barnes did against Matic could have resulted in a severe injury (hence the reaction of both Matic and Ivanovic). Players know damn well when something is dangerous. IMO English referess are irresponsable in this aspect: they often don't protect the players. English football is supposed to be "more physical"...but what Barnes did yesterday should never be tolerated on a football pitch.
All this said, Chelsea do have a right to complain, but Chelsea should always win this match regardless of referee decisons. They didn't help, but a team like Chelsea should always win against Burnley.
And about the complot theories: my 14 year old daughter is a Chelsea fan. When i tell her that there are Chelsea fans who seriously think about acomplot against Chelsea, she has to laugh with it.
PS: i haven't seen the beginning of the match, but wasn't there an anti-racism action of the Chelsea fans before the match. Isawsomething about it ona Belgian website.