Provincial birth registries, from which the Statistics Canada numbers are drawn, are not "managed by each hospital" nor are they "very poor records." A person's birth certificate lists their place of birth and the details of the parents.Not on gut feelings. The hospitals with NICUs in greater Montreal, Vancouver and Toronto end up having unpaid bills of often hundreds of thousands of dollars and having to write off the costs most of the time and we may be paying to send those with provincial coverage to another city of country. If someone is pregnant with multiples and they are likely to deliver preemies early but the NICU is full with sick babies who are unlikely to be discharged soon they move the mother, sometimes to the US, in preparation for a potential delivery so they know they'll be NICU capacity. Canada does a very poor job at keeping records of FN use of healthcare. It ends up being managed by each hospital.
https://www.cbc.ca/news/canada/birth-tourism-strain-1.5413296
If Statistics Canada is able to draw any inference at all from provincial birth registries about the immigration status of a child's parents, I trust it to be true.
Now, if they're guesstimating, because somehow the provinces do not properly track information, then that's different.