Actually I don't know who is right... cause my rocks came with coralline to begin with... But I wouldn't be surprised if the algae got some spores or something that is suspended in seawater so no need contact to spread...
Ah... good good. Get the "paper" quickly... just don't be disappointed if you later find that the "paper" actually not that great in reality...
No wonder you have been on such a buying spree recently.