I have been using the Amazon LSD High Capacity AA cells for several years and have had no problems with them. I, too, believe that they are re-badged Eneloop XX cells. If you buy eight at one time, rather than four, they are about half the price of Eneloops, which works just fine for me.
One thing I did learn. The Amazon cells to much better in higher drain devices than alkaline cells. I have the Energizer Folding LED lantern, the one that takes either four or eight AA cells. When I used it with the four alkaline cells that came with the light, it started to act real weird. After some use, when I would turn it on it would turn off almost immediately. If during that little interval I would dim the light, it would stay on. After I replaced the alkalines with the NiMH cells, my MTS Mini tester told me that the alkalines still have 50& of their capacity. I have yet to have that problem with the NiMH cells. Apparently, alkaline cells under high drain sag their voltage much faster than NiMH cells do, which would be another reason for switching to NiMH cells.