I think our understandings differ. Periphyton is all the micro-organisms attached to underwater surfaces. One online dictionary has this definition...
“freshwater organisms attached or clinging to plants and other objects projecting above the bottom sediments.”
To me that includes mud, sand, rocks, wood, plants, algae, (heaters, filters, pipes, cables, glass...).
Filamentous algae can form huge clogging clumps which would no doubt be host to many micro-organisms, so I would consider that very much periphyton.