> We have proof from studies that rent control actively makes things worse for everyone

There is rent control everywhere in Spain and it didn't make anything worse. For some reason this 'rent control make everything worse' always originates from the Angloamerican financial discourse. And not surprisingly, the reference you gave is from a neoliberal institute...

I am Spanish, and I can tell you there is a lot of Spanish media claiming rent control is making things worse in the cities that implemented it. Just do a Google search from within Spain: almost all the results discuss negative impact.

Try this search search: control de alquiler barcelona efectos

They are saying it... is it true? Or is it just propaganda?

This anecdotal, but rent control sure was nice in Santa Monica when I lived there. I could have never stayed there as long as I did if not for rent control. Neither could any of the old ladies in my building. Everyone aside from the land lords seemed to love it.