How much should we trust investors when they say they will pull the trigger after they speak to a reference and they actually do?

In my past experience, even after great due diligence, it doesn't mean they will necessarily invest (as when it goes to the partnership, some partners may ding). Your customers have limited time and you may not want to loose a reference call, if the investor is not serious. You should try to leverage this opportunity to ensure they have done all other due diligence and they are serious before connecting ... Sometimes, you'll notice that investor may back out on the call (Which is again good as you know where you stand).