No, what he was told may or may not reflect her feelings, but the order came from somewhere. I don't need you to tell me that I need to learn about her or about history, thanks. I'm sure you didn't intend to come off as condescending, but yeah, you do.
Leaving that aside, I can only speak to my experience. Yes, there are always people who use position and power to create conflict, but that's not the point. And I will give the late queen credit by saying that in later years, she did not appear to be racist at all. Of course, there's a span of more than 20 years between my father's experience and my observations. People can and do grow and change.
The point is in my experience, it's not uncommon for the "white side" of the family to question what colour the baby will be or to express concerns in that regard. I've experienced it and I believe Meghan when she says she did because it rings true. I'm not saying it came from the queen. I can't say where it came from, but it came.