EU referendum, brexit and the aftermath

According to their data, no - the company is fully held by the 'Bund' or the 'Schweizerische Eidgenossenschaft' (Swiss Confederacy), which is the government at federal level. By the way, there are other companies also providing rail services such as the BLS, owned over half by the Kanton Bern and over 20% by the confederacy.

(Oh, also, the SBB itself in turn owns a whole host of other companies either fully or partially, such as SBB Cargo, a catering company, and some regional railways.)