ok, understood and thank you Ron. So, to summarize:
1. I have WP multisite up and running as the single hosted site in my hosting account, and also with a static IP address.
2. I (think?) I have to also edit wp-config.php and add: define('COOKIE_DOMAIN','');
3. Customer requests and receives a new blog instance in the multisite network: customer.mymultisite.com
4. Customer registers a domain www.foosite.com, and at registrar he sets a CNAME record to point www to customer.mymultisite.com
5. I go into admin for customer.mymultisite.com and set the URL to www.foosite.com
Then, everything works as expected - all URIs using www.foosite.com will work. If this is correct, then I'm home free. I will give it a shot if you don't think I'm missing anything.