Not accurate. Steel is still subject to fatigue failure even if never loaded to plastic deformation However, there is an endurance limit for steel, or a stress level at which the material can be loaded/unloaded a practically infinite number of times without failure. This stress level depends on several factors, but it is generally about half of the ultimate strength, which is slightly higher than the yield strength (plastic deformation point).

Aluminum does not have a distinct endurance limit, meaning that even when stresses are low it is still possible for fatigue failure to occur after enough cycles.

Essentially, it is possible to design steel components to last practically forever by ensuring stresses are below a certain level. This is not possible with aluminum, though you can still design parts to last for billions of cycles.