Wow, I am not sure I agree with that statement at all, but this might be an example of defining our terms. For one thing, windowpane checks really don't look much like plaid at all, except for the whole right angles thing. Though a little bit out of period, William Mosman's 1749 portrait of John Campbell shows a fairly simple plaid that is still complex, compared to checks*. I think it's more accurate to say that plaid is much more like multiple checks overlaid next to each other. So I guess I should ask you what you think of when you think of a checked pattern?
I don't care what you wear, nor do I think it is unreasonable to wear a tartan coat, but I don't think it is accurate to say that a tartan coat IS a checked coat. Your coat, however, does look GOOD.
*Being a Campbell, though, it's entirely possible that portrait is compromised by the subject's untrustworthy and devious manner.