I have done crossfit in the past and have many friends who still actively participate. The majority of them do take paleo literally.
The reality is, I think, that it varies from box to box, community to community.
I don't find carbs in any form particularly satiating. Unless I have protein and/or fat with a meal, I'm hungry quickly after. So steel cut oats, not satiating on their own. But if I add say crushed walnuts to the oats and have a couple eggs or greek yogurt too, I fine almost till dinner. The more refined the carbs, the worse it is for me.
One observation is that if you were running everyday(I'll assume you mean that literally), then you weren't giving yourself time to rest and recover, which may be why you are experiencing your pain. I hope you recover soon!
Having said that though, if you are experiencing knee pain(and I can say I've had my share), you're doing the right thing by resting and taking up swimming. I'm not much of a swimmer at all, but getting in the pool and being able to work out despite having hurt myself felt like heaven.
I did run literally everyday. I stopped completely now. Hopefully I should recover soon.
I'd rather eat fruits and vegetables, yogurt, cottage cheese, eggs, fish, etc.
To be clear, I don't avoid grains entirely. I'll have a slice of toast with 3 eggs at breakfast, or put homemade granola in my yogurt, etc. I eat rice with sushi or chicken tikka. Challah is one of my great weaknesses. It's just that grains are so readily available and easy to eat too much of, so I limit them when I can.
Aside, I don't think carbs are evil, but they are very energy dense and not particularly satiating, especially refined carbs (i.e. carbs not from produce). I run 60 miles a week, crossfit 3-5x a week, and still have to pay attention to limit calories from refined carbs.