Exactly.
The objective criteria are so restrictive that it's quite easy to determine which people have this right in a community. It's an advantage in negotiating a place, a school, or building a new school.
However, these same marginal criteria in turn exclude all sorts of members from the English-speaking community. There are families of Scottish descent and others who have undoubtedly spoken English for decades, but whose subsequent generations have legally lost the right to attend anglophone schools simply because some members of their families attended francophone schools in the 1960s.