So what you are saying is that you or your company can't deliver services that you or your company promiss so it's your customer's fault for not buying additional services from other people that can?
That's not what he's saying at all. He's advising you to not put too many eggs in one basket. I'd be more inclined to trust a company that gives such advice, because it's good advice.
If you have all your data and DNS stuff locked up with one company and you want to switch to a new provider, you're at their mercy. If they go under or have a management change that inspires them to be less responsive, you're screwed.
If you use one company as registrar, another to host your DNS, another to host your live site, and another to host your backup, more people have to screw up before you've got an irretrievable mess. If the ones hosting your live site screw up, you can replace them with somebody else, repoint the DNS with your DNS provider, and restore the data from the third-party backup provider. Good luck doing this if you put all your eggs in one basket because the provider assured you they were competent and there was no need to hire anybody else.
Replaying this scenario with screwups on the parts of other parties in this arrangement is left as an exercise for the reader. Alternately, you could just place all your business with the same company and wait awhile. Eventually you'll be pulling your hair out one night saying to a coworker "If only we had placed [blah] piece of this with another provider, we could have had the site back up by now..".