Yes and no. While virtually all multi-rail PSUs have all their +12V rails fed by a single transformer and rectifier, the rails themselves are on separate transistors, which does provide a level of EMI filtering and short protection. There's also a limitation on the current that can be provided by any individual rail (OCP). It is therefore possible to overload an individual rail while still remaining within the total output spec of the PSU, hence multi-rail PSUs are questionable for systems with an unusual loading situation, unless you know the specifics of the rail distribution.
The TPIII is essentially a single rail unit - there's no OCP on any rail and no proper separation of the wire groups. While all Seasonic built units behave like this, this is not the case of most multi-rail units made by other manufacturers..