upon presentation and surrender of the original notice to pay sent to the Tenant at the request
of the Landlord (supporting documents included), provided that it is enforceable and no
appeals, even partial, have been lodged, or it is accompanied by a final and enforceable
judgment that dismisses the original appeal;
So to make a claim through Swisscaution, the landlord simply has to assert that the claim is "enforceable", there is no prerequisite that he obtains the court order.
It is not clear what they mean by appeals, for example, whether Swisscaution will notify the tenant and give an opportunity to contest the matter or whether the tenant has to send a registered letter disputing the claim.
With a bank deposit scheme, the bank will not release the money to the landlord unless he takes the extra step of proving his claim in court (or obtaining the tenant's consent to deduct money from the deposit)
So with Swisscaution, if you have a slightly unscrupulous or opportunistic landlord, he has a shortcut to get this money.
In article 6 of the PDF:
If SC pays a sum to the Landlord in accordance with the rental guarantee, SC is immediately and
fully subrogated to the rights of the Landlord and is entitled, by means of a payment notice, to
seek reimbursement of any sums it has paid to the Landlord under the agreement, together with
administrative costs of CHF 100.- plus interest.
This substantiates the remaining part of the original post: that after Swisscaution pays money to the landlord, they go after the tenant to recover that money (plus their fees). Presumably as this is the focus of their business they are more highly optimized at pursuing such debts than a landlord on his own.