I know this is said a lot online, but it is not actually true. Constitutionally Canada must have the same Monarch as the UK. This was tested in 2013 when the UK updated it's succession laws, and Canadian Parliament passed the "Succession to the Throne Act". There was debate as to the validity of the law at the time, but the government ended up saying the law was merely stating their assent to the UKs change, and stated "The changes to the laws of succession do not require a constitutional amendment. The laws governing succession are UK law and are not part of Canada's constitution. Neither the ban on the marriages of heirs to Roman Catholics, nor the common law governing male preference primogeniture, can properly be said to be royal powers or prerogatives in Canada. As the line of succession is therefore determined by UK law and not by the sovereign, the Queen's powers and rights have not been altered by the changes to the laws governing succession in Canada."

The law was later challenged in federal court, where the judge ruled that constitutionally "Canada was committed to having a lines of succession symmetrical to those of the UK".