Yes, this is definitely a failing in the capitalization rules. A sentence like:

“Get out of here!” he shouted.

will be flagged as an error because the “he” is lowercase, which it indisputably should be. It’s too bad, because it is a useful thing to be able to check for bad capitalization. I don’t want to turn off this check, because the program did pick up one error using this rule where I had typed a lowercase L at the beginning of a sentence instead of the word “I”, but most of what it flags is correctly formatted quotes.

A similar situation applies to double words. It doesn’t surprise me when it highlights “had had” (“He had had measles as a child”) or “that that” (“I knew that that was an error”). But it also flags double words separated by punctuation, which is rarely a mistake. (Eg, it flagged the word “it” in “I cannot describe it – it was as if someone had spun me around”)