Exception that proves the rule
"The exception that proves the rule" is an exception to a generally accepted truth. This is an archaic use of the word 'prove', which means 'to test'. It does not mean that it demonstrates a rule to be true, but that it tests the rule. It is usually used when an exception to a rule has been identified: for example, Mutillidae are wasps without wings, and therefore are an exception that proves (tests) the rule that wasps fly.
"The exception (that) proves the rule" also means that the presence of an exception applying to a specific case establishes ("proves"

that a general rule exists. For example, a sign that says "parking prohibited on Sundays" (the exception) "proves" that parking is allowed on the other six days of the week (the rule). A more explicit phrasing might be "the exception that proves the existence of the rule."
In short, the article is cheerleading bullshit. The energy situation in these five tiny nations "proves" nothing of the sort.