There is no such thing as "absolutely, perfectly, 100% safe."
Each tool has its proper and improper uses, and each works either in parallel with other tools to increase safety and dependability, or in series with other tools ultimately reducing safety and reliability.
Will a hydraulic jack hold up a car safely? That depends on the level of risk you're willing to take. In a hydraulic jack there are several failure modes:
- Structural failure (metal fatigue, fastener failure, weld failure)
- Slipping, falling
- Valves (3 - release, and two one way valves)
- Improper assembly/maintenance/fluid
Further, some of these are slow, almost imperceptible failure modes. If the seal or a valve leaks slow enough that you don't notice, you might start work, not discovering until too late that the vehicle is lowering and finding yourself unable to extract your body from the slowly lowering vehicle. If you're lucky you can call for help. If not...
If you have confidence that all of these are acceptable risks, then sure, for your definition of safe perhaps a hydraulic jack is "safe". I wouldn't trust my life with it, I wouldn't recommend it to any others, but if it's just you then not even the government can force you to employ better safety practices.
Let's look at the jack stand failure modes:
- Structural failure (metal fatigue, pin/ratchet failure, weld failure)
- Slipping, falling
There's simply not too much that's safer than a jack stand in terms of supporting a vehicle... except more jack stands.
For me, though, this still isn't safe enough. One jack stand means one failure - thought perhaps unlikely - could result in injury or death. So at minimum I continue to use the hydraulic jack and a jack stand, but more often than not I'll use two jack stands for each lifting point and remove the hydraulic jack simply because it takes up so much room.
What you really need to determine to answer your question is what is your level of acceptable risk, and what's the cost. If you experience a failure, what's the cost of the failure? Given that your life and limb are involved, the cost of failure is so high that, for me, the extra time and cost of setting up a jack stand is always worth it.