Let them monitor themselves (Score 1)

There are plenty of free services that will allow them to monitor their website Uptime is one of them. In one check then can monitor their website AND their DNS service. Heck, tell them you'll sign them up for the service if they like (most are available for free). Why not utilize (or tell your customers) about a free service that can help both of you out?

Why let a third party come in in the first place? When you can spend a bit of time proactively to make your customers happy and avoid the whole mess.