They are test standards of the parameters used by the chip manufacturer. Your application might very well be different. If your application falls within the generic specs, then sure. If you are pushing the edge, then you have to look closer. You can still achieve the manufacturer's specs if you use proper designing techniques.
For example, when a data sheet states that the device will work between -40C and +150C, they usually list a min max and typ to show their results. What they might not tell you is that 50% dropped out at +142C, and thus they can still compete with their competitors and advertise the +150C top end tolerance for temperature. But if you are manufacturing this device to be sent to the equator, you will want to provide more testing before you package it. This would be considered an extreme for any company. If you are using the device in your lab, you are pretty safe with the min tolerances given in the data sheet.
So, in answer to your question, yes, you can rely on the specs. If your application is extreme, you might have to add something to the circuit to continue to achieve this.
MP