Your 1st point is true...however your 2nd point is not.
Even though the probability is very low, technically you can get variant CJD from eating any part of an infected animal including the muscle tissue. By far the highest concentration of infectous prions are found in nerve tissue,ie the brain and spinal cord.

Just to put things in perspective.......the odds of contracting VCJD(mad cow disease), even after consuming large quantities of infected beef, are still incredibly small.

Back in the 90's Britain did have a mad cow "epidemic" and a large percentage of the beef was infectious, especially the hamburger. The greater majority of Britain's 75 million residents consumed large quantities of infected beef for approximatly 9 years.
Out of that 75 million people only about 100 ever got the disease!
World wide only about 135 people have ever gotten the disease. And in the US only 3 have ever gotten the disease and all three of those lived in Britain for a while.
So someone else is welcome to calculate the odds but basically....even if you happened to eat an infected hamburger the odds are greater that you will die in a bicycle this week than from "mad cow " disease in your entire life!

While we are at it there is one more myth that needs to be corrected.
Back in the 90's some "scientist" got a lot of media attention when he started claiming that the incubation period for VCJD could be up to 30 years. This has since been proven wrong. If it were true we would be seeing larger numbers of cases every year. This is not the case....the number of new cases have dropped to almost zero anually worldwide!

As a final note....aside from the terrible loss of those that did die from this disease and the grief it caused their loved ones, the damage that this caused to hundreds of thousands of small farm and ranch families was truely devastating. Many were needlessly driven from the land to be replaced by large corporate run grain farms.
Support and get to know your local family run farms.