Thats exactly it, you have flipped the burden of proof.
The group making the statement does not have the onus of providing proof that disproves their own statement. This goes for all logical statements. The proof of actual satanist doctrine (What that actually is and where in their dogma it resides) within the TST in a logical argument would be something that you would need to provide in this context. Otherwise the request is illogical and their point stands that they are as legit as any other religious entity until proven otherwise.