The FADP does not say that data must stay in Switzerland. It says you remain responsible for its security and that any disclosure abroad must be covered. The definition of disclosure includes making data accessible (Art. 5 let. e): remote access from abroad, for technical support for instance, deserves a look as much as the location of the servers.
Hosting in Switzerland simplifies the analysis: no transfer to justify under Art. 16 and 17 for the storage itself, and a known applicable law. It does not remove all legal exposure. A Swiss host remains subject to Swiss law, including international mutual legal assistance, through which a foreign authority may request data under the conditions of the law and the applicable treaties. A provider that belongs to a foreign group, or uses a foreign sub-processor, may also be subject to another legal system.
Location is therefore one criterion among others, to be read with the contract, the list of sub-processors and the security measures. For a specific question, the Federal Data Protection and Information Commissioner publishes guidance, and a lawyer or your data protection adviser can assess your case.