The few hundred number was cited to STATCAN, your opinion about "likely thousands" is not.
GIGO. Statcan can only base its numbers on what hospitals report, and hospitals, for the most part, are not reporting. Nor is there anywhere on the form to report citizenship. But if a Liberal MP says over 300 foreign births took place in one Richmond hospital in one year I don't think it's out of line to presume there are many more of them across Canada.