Another counterexample is the Eastern Brown Snake of Australia (see notes). It has the double caudal scale row pattern of the "nonvenomous" picture.
But the counterexample is not my main point. I'd like to raise the following line of reasoning as an indication of why you should treat any assertion such as this with extreme skepticism. And that reasoning is simply to ask yourself how any creature gets to be venomous. It gets that way because of evolutionary drivers: initially through random mutations, its saliva or other bodily fluids exchanged with a foe - either during defense against an antagonist or during bringing down prey - contains proteins or other substances that subdue that foe. This might be, for example, mouth chemistry that is friendly to symbiotic bacteria that produce tetrodotoxin, as in the blue ringed octopus. This effect conveys an evolutionary advantage that is then re-inforced by natural selection.
Now, ask yourself how plausible it is that the same evolutionary drivers might affect the skin patterns on the tail at the other end of the body. It's not plausible at all. If there were a relationship such as this picture alleges, there would be a very strong evolutionary explanation for the link (albeit it may not be causal). For example, venom use requires a means of delivery, so it is vaguely plausible that venom carriers might have general facial shape traits. However, none have ever been observed: effective fangs fold up so neatly as to have no effect on the animal's facial shape.
Eastern Brown Snake (Pseudonaja Textilis): This one is particularly and extremely dangerous; owing to its venom's action on the blood, you've only got a short time to get the antivenom or at least make sure a compression bandage / limb immobilization is properly in place to stave off a likely fatal outcome. Basically its venom wreaks the same havoc as a massive intravenous injection of factor X would bring about.