I would disagree. Understanding how a song is constructed is the first step on the road to being able to steal the technique for your own songwriting.
In this case, classical theory actually does cover this. If a piece or section is in a minor key (Am in this case) and finishes on the tonic, the third of that chord can be raised chromatically, changing the chord from minor to major. This effect is called the "Picardy Third". If you look this up, and look for a few examples, you'll see it's very common in the classical canon.
More detailed explanation here:
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This major chord is carried over into the chorus, and you could consider it as a borrowed chord from the parallel major, or just an extension of the resolution of the prior section. Either way, it sounds pretty great when the C# in the A resolves chromatically down to the C, as friendlybass said.
It's a lot easier to NOT use classical theory to try and analyze this. Use commercial (or jazz) concepts and get away from diatonic reasoning. It takes like 15 more steps to explain a chord progression if you think of it in classical terms. I know what a picardy third is, but I don't use that term when playing commercial music. Also, "borrowed chord from the parallel major"???? I get that, but we aren't talking about Mozart here. It's Soft Cell, and it's commercial music. There are easier ways to explain songs like this with music theory. Using classical terminology isn't one of them.