That is not true. A hydrotest fills the tank with water and checks how much the tank expands under pressure. If it expands too much it will fail but it may still capable of holding pressure. The idea is to prevent it from failing under pressure.
Tanks decades old can still pass the test.
Almost true. I used to hydrotest CO2 tanks (and other high pressure tanks like scuba tanks) back in the '70's in FL for a fire extinguisher company.
A hydro test procedure is to fill the tank with water, stick the tank in a closed water vessel so you can measure the tank volume before and after pressurization. Pressurize the tank, measure the volume the tank expanded, then depressurize.
After depressurization, measure the tank volume again and ensure the new volume is not more X% (don't recall the exact number, but I think it was 10% but don't hold me to it) over the original. Essentially you are measuring the ductility of the tank material.
I personally tested tanks that were dated back in the 10's and 20's and tested just fine. The scariest tanks were the aluminum scuba tanks where you would pressurize and watch the volume keep rising once you reached test pressure - indicating the tank was getting ready to blow.
We tested all failed tanks twice (unless it's one that keeps expanding) because we had to permanently mark the tank and it's usually a big expense to replace them. Customers were never happy when we told them their tanks failed... especially if they were planning a big scuba vacation or whatever.
However, getting to the issue at hand: I've both leased and owned high pressure C25 bottles for the past 12 years. In both cases, the refill companies just exchange the bottles, they don't care about hydro testing dates and what not. Even my "owned" tank gets replaced when I need it refilled, which is just peachy-kean for me - never have to worry about paying for a hydro or worse - a failed tank.