We have a strong policy about advising clients like this up-front something like: "Of course we're happy for you to manage/engage your own web hosting. Are you going to be using them or us for first level support in case of problems? We're happy either way, and our usual $150/hr hourly rate, but if you'd like us to be the first point of contact you'll need to supply us with details of your support contact at the hosting company, and authority to incur support cost with them when required."
I simply inform them in a candid way what the problem is, and if they're reasonable they'll probably switch services or find a way to accomodate. Otherwise if I detect a tendency for cheapness, then I know there either needs to be a longer discussion or that they are in fact a red flag.
Sometimes it's also a pretty good discussion early on to help to start getting the feel of the type of respect and consideration potentials clients may hold for the consultant's advice.