If a proctologist report would be of any value to me I would insist on it.

If they insist on this point, or any point that seems odd, then you've probably discovered their game.

He insists 30 days written notice, which I argued was not possible because of his late notification of rent increase.

They will insist he never shores at home (only the gym), etc. etc. if they fight back, maybe $50 wear and tear, $50 for water.

They've only been in the house for 6 months and have consistently tried to pay late every month (I have insisted on on-time rental payments, and they have complied, but grudgingly), brought a dog in despite a "no pets" policy, and are generally stand-offish (the first thing they did when they moved in was install a security system, and when I come by the house even with an appointment, they call me while I'm on the front steps and say that they're not in the house). 

She insisted her dog wasn't a pit bull and she hadn't chained it.

AND insist that the sister understands the rules she must abide by as a new "resident".  

Do you find in number 3 that since it says "postmarked on or before the 1st of the month to avoid late charges" that if you don't have it by the day it's late, tenants just insist it's "in the mail"?

Usually, the tenants invite me in while they are paying me, so I get to see the inside of the home.I understand that some landlords might not want to pick up rent payments, but I don't think it's fair to insist existing long-term tenants conform to your new payment plan.  

He refused to communicate with my broker, insisted that I hire an attorney to communicate with him, and then told my attorney that he was jerking me around because he knew that it would cost me more in legal fees to fight him than I was entitled to get from him.