Killer,
Sorry I fell out of the loop on this one. I have to say that Takeshi has done beyond an above admirable job on laying out the issues of how referrers become direct. I think two things stand out to me: yes the installation of your GA code could be wrong and it should be before the closing head tag . Often people will put it in the footer and occasionally someone enters it more than once.
I think another thing you have to look at is you are comparing Chartbeat to GA and they provide two types of analytics. The numbers, of course, are different. Chartbeat was out before GA had realtime and, I think, it was intended for the real time needs. It claims to have better data for publishers and I have no way of comparing. Since it has been around for some time, I would think it has some real traction, but you have to be careful as you are comparing two different services.
Another thing that gives me a slight amount of concern about the issue is that they have a section on how they help you sell more ads (when you are a publisher). That type of data makes me a bit nervous. It may be the real deal, it just makes me nervous when something claims to help you prove your position.
The question re your site is a bit skewed in the way you present it. What is the other data re that site? How many total directs? How many organic visits? How many PPC visits? Etc. You cannot just conclude that there cannot be that many directs without all the data. How many total visits would be the first place to look.
As to the expert on analytics and your GA code, you can do it your self. Look at view page source (typically a right click function). When you have the page with the code on it, do a control lookup (command or Control plus F on). Then in the search box, type in UA- and see where it occurs. There should be only one occurrence of UA-XXXXXXXX-1 or -12, etc.
If you see it more than once it is likely a problem, but not always. If it is in the header and footer, typically you will see an artificially low 2% or less bounce rate. You can also do a lookup of the closing head tag and see if it is after the analytics code.)
I hope this helps you a bit.
Robert