I have to agree with Gary on this one. If they tell you its OK to jack under the axle only in certain places, then someone will (with an attention deficit) will read the "its Ok to jack under the axle...." and miss the part about only under the spring perches or within 3 inches of them. So they just say, no, don't.
Trying to reach the frame of many trailers indeed would take a very tall jack. On my recent trip to Lake Charles, I discovered on my buddies trailer, a spring hanger torn off the frame. He had his RAM screw jack, and a bottle jack, I had my RAM screw jack, and a small bottle jack, any of which will go under the axles, BUT, I had taken a two stage Mercedes Sprinter bottle jack that while limited to about 7000lbs, goes quite high. I stuck it on top of the 6x6 block I usually put under my tongue jack and we lifted the trailer right up, then we ran his new stabilizer jacks (which are Harbor Freight screw jacks capable of the tonnage) down nearly full extension, to provide a safety. We were then able to get the spring hanger back in place and use a bottle jack to raise that axle to where everything fit and the welder could do his job.
In the shop I usually jack my trailer under the spring at the axle, and then put a jackstand with its U saddle, right under the axle tube as close to the spring as I can get it.
Jacking under the MIDDLE of an axle will most certainly bend the axle (be it leaf spring or torsion type) and you can even bend a automotive axle by jacking under the "pumpkin" (differential) if the vehicle is heavily loaded.
Charles