No, I think you have how it works wrong in your mind.
This is how I use TeamViewer.
I have an account.
On my customers' computers, I install the personalised version of TeamViewer Unattended Host.
These are automatically added to my list of 'Computers and Contacts' in a default group that I have set.
I have a group for each 'customer', each of whom has multiple computers.
On ANY computer where Teamviewer FULL is installed, I log into my account, and move these auto added computers to the group that represents my 'customer'
If someone, ie a new customer, wants me to access their computer, and they already have Teamviewer installed, or the download it from the Teamviewer website, I simply type their TeamViewer ID into the 'partner ID' on the Teamviewer Full that I am sitting in front of (or use the web portal supplied by TeamViewer), and the relevant password. Done!.
If I were to want someone to log onto my computer, then I give out my TeamViwer ID and a one-off password.
They don't need my unattended access password, or my permanent password, unless I want to be able to log in again later.
The management reporting Beta from the website is just brilliant.
I set a default rate and some defaults about lengths of connections etc.
I can set a customised rate per customer.
At the end of each month I check the usage to each of my customers, and essentially generate an invoice based on connection times etc. I can save or print to pdf, or even copy and paste into excel.
Does this clear things up for you?
Matt