You cannot be offside on a throw-in actually. You're sorta demonstrating the point of inconsistency of understanding of the rules (intentionally or otherwise). A goal cannot be scored directly from a throw-in, but it's either a goal kick or a corner kick, depending on the goal it goes into (as later stated). Etc.
Your initial point is correct and on-point, though: those are the only rules related to throw-ins. The call in my son's game was a pure fantasy delusion; there was no infraction. These delusions and incorrect calls are very frequent, though; probably more frequent than any other types of incorrect calls in matches.
One other oddity with throw-ins (while we're referencing specifics in the rules), which I find interesting at least:
In soccer, the lines are generally considered part of the field, the width of the lines is mostly unspecified, and the ball must travel entirely out of play to be out (ie: all parts of the ball over/outside of all parts of the line). When I was growing up, the laws specified that a throw-in must be taken from outside the field of play; touching or going over the line (ie: entering the field of play) before releasing the ball was an infraction. This is not the case currently, however: in the current rules, both feet must be not entirely over the line, but as long as one or both are touching any part of it (or behind it, of course) until the ball is released, the throw-in is legal. Ergo, in the current rules, the player taking the throw in can be entirely inside the field of play when the ball is released (eg: both heels touching the inner edge of the line), and it is still a legal throw-in. Them's the rules.