It is a general 'rule of thumb' that guides procurements and deployment planning for all classes of warship. Donitz used it in WWII when developing his estimate of how many U-Boats he would need to achieve effective tonnage-war against the UK. Other modern navies continue to use it, but with modification: eg for critical units such as SSBN required to maintain a continuous at-sea deterrence presence, the ratio might be 1:4.
In times of crisis, the rule can be bent - a ship coming out of refit and doing its pre-ops work-up can be put through an accelerated process. But as you note, it would depend very much on the kind of refit. If it was a major dockyard overhaul such as a mid-life extension, with works such as engine replacement or fitting of major new systems, then the work-up period would be far longer. The more experienced navies know that any acceleration of the process or corner-cutting tends to be a false economy, with ill-prepared crews and systems rendering the vessel less than effective when it comes to the test of combat - to cite the U-Boat experience again, the survival rates of U-boats and their rates of sinking declined sharply as boats and crews were rushed into service as the war dragged on. And in any sustained campaign operational defects can account for more assets being unavailable than combat losses. The RN at the same time was able to maintain far more extensive pre-operational work-up training for ships entering commission, with training becoming, if anything, longer rather than shorter.
Resource-poor navies are always going to face a challenge - they can husband their limited number of ships by cutting back on peace-time sea-training and cruises and the associated wear-and-tear, but they then tend to pay the price with lower crew experience when mobilised. Some navies, such as the Soviet, tried to overcome some systemic crew deficiency (conscript sailors) by adopting higher levels of automation and more technological solutions (a guided missile requires far less human input over its operational life than a carrier strike aircraft).
Hope that gives some context