lol, she is full of it,
as for recharging alkalines, well, try it yourself, you'll see, we can go on forever, with he said, she said.
if a load is few hundred miliamps, than alkalines AA will have real capacity close to rated, at high loads it will be greatly reduced, proportionally to the load.
as for D cell capacity of alk. D is around
12ah, rechargable 8-10, at loads of 1A and less, capacity will be close to 12ah, at higher loads, same story as with AAs, nimh\nicd will not lose nearly as much capacity as alk. they can give 10A with small loss in capacity.
for the most part rachargable D you see in the stores, (retail stores, not web sites) are not really D cells, they are AA in D case, and usualy made by who knows whom, it is done for a few reasons, price, and ease of charging, since there really are no chargers for consumer use that can properly charge 8ah cell. so a duracell AA at light load might have larger capacity than D with AA inside, but it doesn't apply to true D cells.
1 thing i might be wrong about, (spoke too soon) is actual runtime difference of alk. D and nimh D in your particular case, if your lantern draws more than 1A than nimh will last longer, if less than there will be not much diffference.