There are many problems which can happen, where the website hosting company can't – and won't – help you.
There are many ways in which disaster could strike your website. If something awful happened at the server end, you'd probably just have to hope that the website hosting company has a disaster recovery plan, and can restore everything for you. You're probably in their hands on that one. However, what about if they just stopped operating tomorrow? It's possible. And it would be down to you, in that case. Have you got some sort of an independent backup of your website?
There are also many other, smaller, problems which can happen, where the website hosting company can't – and won't – help you. I'd be prepared to guess that most businesses have stuck their heads in the sand on this one, not even daring to consider how they might retrieve such a situation. What I'm talking about here is more to do with human than technical error. Many content management systems allow you to mass-delete pages. It's easy to accidentally overwrite a page or an image, just as you can do with a document on your PC. I've seen hackers take over websites and delete swathes of content indiscriminately. I'm sure you can think of more potential problems which could be caused. What would you do?
With my content-managed sites, which are all based on WordPress, I have installed regular backup plug-ins, which quietly make copies in the background every few days. With the few sites I run which are just a collection of static pages, I make copies of the entire sites from time to time using an OS X utility called Sitesucker; in the past I used a Windows application called Internet Download Manager. There are many options, but the important thing is that you've addressed the problem of what you might do if all or part of your website went missing.