That is correct. A Knight's Raiment is projected at age 9-10 and is the perfect weapon for the Knight who uses it. Now who is to say he didn't project his family's heirlooms? Or at least Weapons that looked like them. I can't speak for where the actual weapons might be but perhaps those aren't actually them? Maybe because he has been so distanced from his family he's never even seen the weapons, just their names and that they exist. I don't know, and it's up to Rai to determine that.