Jim, Your reasoning and example are pretty clear.

'A semicolon is best used to link two phrases that grammatically could be separate sentences, but that need to be linked together somehow to show their proper meaning. For example:

I don't care what the dictionary says; I like the word "irregardless."'

But the meaning of this sentance would be clear (IMHO) if you used a comma rather than a semi-colon. What's the objection to this?