In formal logic this is called a Disjunctive Syllogism (sometimes called 'the process of elimination' in informal logic) - grandchild of the syllogism a la Aristotle you've got going on with the green man. As logically valid as they come, this one!
Formally if one knows: 'X or Y' and 'not X', one may conclude 'Y'
It's often difficult to find the premises in practice for anything non-trivial (it's easy with different colours of paint, but try listing different theories of electron behaviour!), but as with all logic the conclusions follow irrefutably from the premises if they are there. (Unless of course the propositions under investigation, like certain quantum properties, are not governed by standard logic: but that is another story...)