Really don't / don't really difference [duplicate]

In the Chris Medina song "What are words", he sings "what are words if you really don't mean them when you say them?". I am a non-native English speaker, but to my ears that doesn't sound good. Had I written that song, I would have let "really" and "don't" switch places. I discussed this with my wife who insists the meaning would be exactly the same, but in my mind there's a difference.

I feel that "really don't mean them" conveys that the person uttering the words doesn't mean them, with an emphasis. He really doesn't mean what he's saying. The words go against everything he stands for. The other way around, "don't really mean them", to me means that he says something that he could very well stand behind, but in secrecy he doesn't.

Am I correct in asserting the above? If I am, what could be the reason mr. Medina chose this particular wording, as it doesn't fit very well with what the rest of the song lyrics express?

So we are comparing two sentences:

• "What are words if you don't really mean them", and
• "what are words if you really don't mean them"

I think in general, the "really" modifies the word after it, so the former has the connotation of only meaning them a little bit; the only thing that is eliminated is that you "really mean" them.

In the latter, the emphasis is to the negation, meaning that the speaker is vehemently not meaning them. It's a much stronger sentiment.

On a scale, it would look something like this:

• Really mean them
• Mean them
• Don't really mean them
• Don't mean them
• Really don't mean them

By way of example in a different and self-referential context:

• if you really like this answer then mark it up, and give it a tick;
• if you like this answer then give it a point;
• if you don't really like this answer then just ignore it,
• if you really don't like this answer then mark it down.