Because you can see the IP address it came from
But you can only trust it of you have reason to trust the website that analysed it. I have no reason at all to doubt the authenticity of the link you posted but equally, I have no reason to trust it.
As such I personally would not advocate posting personal email headers into that analysis tool, owing to the potential privacy risk. If you are personally acquainted with the website operators that would be different, but I am not.
And even if is genuine, what will the IP address tell you? If it is not one assigned to BT it could still be genuine, if BT had simply subcontracted out the work of sending mass mail shots.