It’s not true. Steel is a non-combustible metal and these rockets are fueled with Methalox. Methane is not an ozone depleting chemical and neither are its combustion products. Physical effects and chemical by-products from satellite re-entry are linked to ozone depletion, so Starlink is the actual thing that SpaceX is doing to fuck it up, as /u/boiledfrog mentioned.

The water vapor added to the air from methane combustion can impact polar cloud formation that might have some impact on ozone layer replenishment, but there’s a lot of complexity there and seemingly even things like groundwater well usage may have impacts on this.