It is not true that everyone who is a PR and residing in Canada is required to file an income tax return.
However, the threshold requirements mandating filing a return are fairly low. And foreign income counts. Who is required to file a tax return is prescribed by Canada Revenue laws and regulations and rules. See the CRA web pages for more information or an accountant.
Even though filing a return may not be required for those with no or minimal income, the benefits structure makes it foolish for anyone to not file a return. Thus, even if a PR is not technically required to file a tax return (such as due to very little income, noting again, however, that foreign sources count), it is so foolish to not file that the fact of not filing in itself invites, at the least, questions if not concerns.
Reminder: the test for being required to file a tax return is not whether one owes any taxes. A person may be required by law to file a return even if that person owes no tax.