As noted above composite tanks have 3 or 5 year re-qualification requirements (depending on the design) and have a 15 year life limit. The re-qualification process includes both the hydro test and a visual inspection. IF, and it's a big if, the statement was made in reference to a hop wrapped composite cylinder with a 15 year life limit and a 3 year re-qualification interval, then the statement is more or less correct. Just more or less, as skipping a few years between hydro tests won't allow you to still have a total of 5 done - the tank will still age out of service at 15 calendar years.
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Some tank manufacturers will provide a 30 year "life span" for aluminum tanks for comparison purposes with composite tanks, but there is no legal or engineering limit applied to 3AL, 3AA tanks and no life limits are applied to exempt, or special permit all aluminum and all steel tanks used in scuba diving.
3AL aluminum tanks do have a fatigue life, but they are tested to 100,000 cycles to test pressure (5000 psi for a 3000 psi 3AL tank) so the fatigue life is somewhere above that number, and that number will be even higher with the fill pressure limited to the 3000 psi services pressure. To put that in perspective, you'd have to fill a 3AL scuba tank twice a day for 136 years to get to 100,000 fills.
There are some dive shops that refuse to fill aluminum tanks older than 20 years, but that's pretty ignorant thinking. I think in many cases it is an outgrowth of the many shops that refuse to fill aluminum tanks made prior to 1990. That is done to avoid filling 6351-T6 aluminum tanks that are prone to SLC cracks, but that date itself was arbitrary as all Luxfer aluminum tanks made after May 1988 are made from 6061-T6 aluminum, and Catalina tanks were always made of 6061-T6 aluminum regardless of age. Some shops have just extended this overly conservative rule of thumb to an even more conservative and totally non-fact based determination of a 20 year "service life" - mostly I suspect to sell more tanks.
3AA steel tanks do not have a fatigue limit and provided they are properly cared for and are not allowed to develop pits from rust, they'll last what amounts to forever, for all practical purposes, with the practical limit really being the ability to find a place to put a new test stamp every 5 years. The oldest tank I've seen come in for hydro test was a welding tank made in 1911, and it was still eligible for a plus rating.