That quote is not wrong, but that doesn't mean there aren't transistors specifically designed for a particular application, switching or linear. It is true that any transistor can be operated in any of the three regions, saturation, cut-off or active/linear, but some transistors are better for switching applications than others.
In a switching application your concern is mainly with the time it takes for a transistor to transit from saturation, through the active region, into cut-off, or vice versa. All transistors can make that transition, but some transistors do it more quickly.
In a linear application, such as an audio amplifier, you never really drive transistors into saturation, or completely into cut-off, and this transition time is of little consequence. You may be more concerned with the linearity of the transistor in its active region, where it spends 100% of its time.
Transistors can't recover instantly from saturation, because it takes time for charge carriers in the base region to vacate, and return the transistor to linear operation, or cut-off. The amount of time it takes for such recovery is a function of junction geometry and doping, and where recovery time is critical you could choose a transistor with better recovery time than others, but you could also mitigate recovery delay by simply designing the circuit in such a way that the transistor is never driven deeply into saturation.
Similarly, if the base-emitter junction is reverse biased, and the transistor is deeply into cut-off, it takes time to repopulate the base-emitter depletion region with charge, and restore it to an active-region state. Again, the solution could be to use a transistor designed to recover from this condition quickly, or simply ensure that the base-emitter junction potential difference is never permitted to become negative, or even approach zero.
So, while there are transistors designed with fast recovery in mind, for switching applications, all of them have the same saturation/active/cut-off states, and they all suffer from the same recovery issues.
In all cases it is a transistor's periphery, those components responsible for biasing and source/load impedance, which are defining whether the transistor is a switch or a linear device, not the transistor itself.
Here are some articles showing the transistor in two different configurations, with wildy differing bahviour, hopefully helping to show why it's not the transistor itself which is deciding its role, so much as the components around it:
These principles also apply to field-effect transistors (where they would be called "common drain" or "common source"). In common-collector configurations, the transistor is always operating in its active/linear region, but the common emitter approach is more suited to switching.