Tweedle Thee and Tweedle Thuh

I find it interesting that there are two words for the indefinite article (a and an) depending on the word that comes next, but there is only one definite article (the). But, there's a special pronunciation rule about the word the that is similar to the rule about when to use a and an: The is pronounced “thuh” when it comes before a word that starts with a consonant sound, and it's pronounced “thee” when it comes before a word that starts with a vowel sound. It can also be pronounced “thee” for emphasis (2), for example if you wanted to say, “Twitter is the [pronounced “thee”] hot social networking tool.” I actually have trouble remembering this rule and have to make special marks in my transcripts to remind myself to get the pronunciation right, so I apologize if I mess it up sometimes. I think I must have missed the day they covered this in school, and I've never recovered.
(Grammar Girl's Quick and Dirty Tips for Better Writing - Mignon Fogarty)

I'm rather surprised that Mignon Fogarty has trouble remembering this rule and that she has to make special marks to remind herself to get the pronunciation right. I wasn't really aware of this rule but I just tried it out for myself and I really can't bring myself to say "Thuh Omega Man" or "thuh effect". This rule comes naturally to me and I don't have to think about it and I didn't learn it in school. I haven't heard anyone go wrong, but then again I haven't paid any real attention.

Are there really a lot of people out there who have problems making the distinction between "thuh" and "thee"?