their factory published empty weight.
Consider what document this would be. If it's a sale brochure, it'll be very optimistic, for dreaming only. What you're looking for will be a weight and balance document serialized to that particular plane. That should be signed by someone authoritative in the company, and state that a weighing was done on date x. Thereafter, when equipment is added (or removed) there should be an amendment to the W&B, which may just be a mathematical calculation, but still signed by someone.
If CASA is advising this, they're either saying that the factory made an error on a number of airplanes, (incorrect scale calibration), or people are referencing the wrong document - sales brochure. If in doubt, reweigh the plane. An airplane flying at an uncertain weight, is most likely also flying at an uncertain C of G position, which could be every bit as serious a situation.