Well, since they can't guarantee that any mechanism will work 100% - I wouldn't trust it.
Most likely, they use a graphic file or a style sheet in the email that they send, and then if the mail reader requests that file, they know that it has been opened interactively.
This would not work on an email sent to me.
Sure, most people probably don't have graphics or stylesheets disabled on their mail reader.
They seem to be using the IP information available in their web logs to track stuff. I dunno - I guess it might be handy if you wanted to try it, but a negative result does not mean that someone didn't read it - so I don't know how much I would trust it.
On the plus side, you may get some data from it depending on the computer skills of your recipient.
Willful ignorance of science is not commendable. Refusing to learn the difference between a credible source and a shill is criminally stupid.
I think you have to ask your ISP what they'll let you do with their stuff. You'll also have to take control of your DNS if you don't already have it so you can point your hostname in the right direction.