Legitimate to me means "legal".
It can also refer to honesty, ie, sellers claims.
Original broadcast sheets are a desirable extra.
Other examples;
A car may have a state issued replacement VIN, it is less desirable from an investment perspective, but not illegitimate.
A car with a missing fender tag would be more legitimate than one with a fake fender tag.
A lot of cars did not leave the factory with any broadcast sheets at all, it does not make them illegitimate or molested.