Roy, I opened your first EPS in Illustrator CS2. Each of the "I"s have both a shape created for the letter (like all the rest of the letters) plus have an additional outline.
A wild guess would be that whoever created this felt that the "I" letters from the original font were too thin, and perhaps they used the outline to make the letter thicker so they matched the rest of the letters better.
I've done that in the past to tweak the look of certain letters in a logo where those letters don't have the uniform look I was after.
But I'm just guessing at the motivation. The outlines are in the EPS, so it's nothing to do with Corel converting the file. Also, because it's just the "I"s I would guess it has nothing to do with Mac vs PC or something inherent in Illustrator. I would think it was done on purpose by the creator of the file.
My guess is that in the original font, the dots of the "I"s were above the top line of the other letters and this was done to reduce the height of the "I"s so the total height, including the dots was the same height as the rest of the letters. In doing that, the thickness of them changed too thin, so an outline was added to thicken them.
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