That's true at the EU level for the inflation measure of the European Central Bank. But national governments tend to have their own (modified) versions of the H

That's true at the EU level for the inflation measure of the European Central Bank. But national governments tend to have their own (modified) versions of the HCIP which do include things like owner-equivalent rent or mortgage rates. Not trying to argue semantics here, your point is completely correct but it may be confusing to say 'the EU (as if, as a whole) considers housing and inflation as separate measures'.