Actually shes right, you do want a better drop out voltage than that.
You also need to consider how low you will allow the battery to go.
If you pull li-ion battery too low you will kill them sooner.
You need to take a long hard look at the battery in question, and the recommended discard level.
Since this chip is good down to 2V, and 2.4V is the minimum discharge for li-ion cells (yours could be higher), you need to figure this out. Also need to know current draw.
For example this
one Which has a max of .2v drop out (it's CMOS rather than bipolar) - if you got the 2V one, it would be perfect (if 200ma is enough juice) as you are not supposed take the battery below that. Leaves some margin.
If you go with charge pumps, you may have noise considerations, but you can longer battery life.