Exactly. You can place a patch with some glue over a hole in fabric to achieve the same thing in a traditional garment. Iron-on repair patches are also similar.
It's one thing to say "get it wet and leave it in the sun". It's another thing to require identical replacement material and nutrient slurry (I don't know about you, but I think I can source fabric glue more easily than potato water).
I guess they're just trying to get the networks to interlace, not to reconstitute into a single organism and be capable of nutrient exchange, so I don't think it matters if they're identical or not.