You Bought It, I Own It
There are some amazing business arrangements out there when it comes to maintaining online operations. In particular is one I call the "You bought it, I own it" model, where your website support person buys your domain and hosting for you, then winds up being the only one with access. You are now dependent on that individual to run your online business.
This relates to the topic "When Partnerships Go Bad" except it's even more serious than discovering misplaced trust; as if you bought a loaf of bread, then had to leave it at the store…with no idea when the store would open again!
Regardless of the reputation a service provider may have, there's more than one reason to avoid this situation.
Website maintenance should be flexible and easy for data updates and content. The business owner that is paying for the site support should be the primary owner of security and, at a minimum, know how to change passwords (accounts, database, whatever is password protected). This at least reduces back doors.
If website content is not kept up to date it will likely mean lost traffic over time. If website data is inaccurate, repercussions might spread all over the Internet.
While you should have the alternative of more than one designated website administrator, too many would defeat the purpose. Two or three people responsible would cover it.
Another precaution is to control your domain name(s). Be sure you can manage, assign, delete and renew your domain registration. This is key for the ability to move your website to another host, for example, or small things like avoiding expiration!
Now, some may differ with the last tip for this article, but I think you should know what you're paying for "under the hood." Technical details can be kept to a minimum (after all, being shielded from "bits and bytes" is often a big part of the reason to hire a technical consultant) but be reassured or warned of what you're getting: know limitations – if any – as well as opportunities for expansion.
If you bought it — you should own it. You certainly have the biggest share of the risks; you should get the largest share of the dividends.
One more reason for ultimate ownership…turnaround. Delay in providing passwords and/or access to other assets can mean huge costs for you. There's inability to delegate or obtain new/additional support. That is time lost without having effective use of what you paid for.