Then, why does it say "use an HTML compatible email viewer"? Well, it is not really said by Thunderbird but written in the email.
It is a good practice for email apps to send alternate text content for html emails. Usually this is the same text but without decorations. However some email producers are ignoring this practice.
Recently, I am starting to receive emails with the text "To view the message, please use an HTML compatible email viewer!". Some of them are just spam. However, today I received one that was of my interest. I searched through the setup and account settings unsuccessfully. Where the hell did I decide not to read HTML emails? Well, if you have forgotten like me, the solution is really easy: in menu View -> Message body as change Plain text for Original HTML.
By the way, if you are automating email generation, it may be worth having a look to some email test service like litmus.