As a Catholic, I've heard that, but I wonder if it's true

It is. Same with all other medieval cathedrals in the UK. Though York Minster often hosts events by other faiths (at a cost) the rite is very much Anglican. Much emphasis is placed on continuity of Christian Worship at these sites, but it's the discontinuity that makes it interesting.

https://www.churchofengland.org/about-us/our-buildings/cathedrals.aspx