Did they actually time (not estimate) the use, is the person reputable, what size, what depth, and are they swimming or just sitting there?
Depending on a variety of factors, you might be able to squeeze 10+ minutes out of a pump up tank, but probably not 10+ minutes of real use, and you'd probably be looking at a 6cu or larger tank. Not impossible, but then we're also dealing with even MORE manual pumping.
I'm not going to argue, but I am telling you what my experience is with small SCUBA cylinders, which I own, and have used all of 19cu, 6cu, 3cu, and 1.7cu. Even on my 19cu, air use is surprisingly fast. I didn't time the dive, but we needed someone to secure an anchor because we couldn't hook anything and were drifting fast due to wind. After a very short dive at 30ft, I managed to use about 1000psi.
If you really want a small tank, I need to get around to selling a 1.7cu and 3cu spare air, and then a 6cu bottle with pony regs. I believe all are out of hydro, but I always transfill them from a scuba-tank. I think the adapter is about $40. Or you could always use one of those pumps.
edit: It appears you are a relatively new diver, which isn't a criticism (we all were there). You can see I actually own some of these mini scuba-tanks. I initially bought the 1.7cu and 3cu as "emergency-devices." After a quick, shallow test-dive on the 1.7 and 3cu at shallow depths, I quickly discovered they're FAR too small to make good emergency-redundant-tanks. The basic experience is tanking a few breaths and then "oh crap, I'm out already?!"
The 6cu, I bought later because I happened across an amazing deal, and they're ok for travel emergency-devices ... if you skip the safety stop and stay above about 90ft. Normally speaking I prefer 19cu (as a backup) at recreational depths. For the 1.7cu or 3cu, if you had to switch over for any reason, you should probably start an immediate emergency-ascent as if you didn't even have the bottle, and will probably run out on the way up.