If they provide reports, check their reports to make sure there are no disruptions in service. A firm that is focused on web design, hosting or other services is probably not focused on online monitoring. Additionally, an online monitoring company should be unbiased and therefore, not affiliated with an ISP or Host Provider. Call or email customer service and see how quickly they respond to your questions. A company that is focused on your site availability should respond quickly to your requests for information or questions about the service.
Customer service is paramount when problems arise.
This may not seem important until your site experiences problems and you need help using the reports to debug the problems. If all of these things are working, then the site is delivering a good user experience. A well-designed service can look for errors in any one of these areas and identify communication errors at ISP's and hosts. You don't know unless you test the service. Don't let your test be the first time you have a critical outage.