A paladin can save lives but to do so requires an act that will make him lose his paladinhood. Wouldnt holding of your code to be more important than the lives of innocent people be an incredibly evil and arrogant idea and thus ground for loss of status anyway?
Again, this goes back to the deontological ethics vs. consequentialism divide that I mentioned earlier.
Paladins (prior to 4e, anyway) were very much based on deontological ethics. Not only did they have work towards good ends, they had to do so by good means. From their perspective, committing an evil act to do good is self-defeating as it would actually help the cause of evil in the long run.
Of course, to someone who takes a consequentialist approach, this philosophy is naive and impractical at best, and evil at worst.
On the other hand, a pure consequentialist approach can also result in acts which not everyone would be comfortable with. It is (relatively) easy to condone the torture of an evil being in order to obtain information which could save thousands of lives. However, what if the information could only be obtained through the sacrifice of an innocent (say, a demon lord - or some other entity too powerful to threaten or defeat - has the information and demands that a child be sacrified to him before he will divulge it)? It could also be used to justify human sacrifice or the torture of an innocent individual (see the Omelas example I mentioned earlier for an instance of the latter) to bring benefits to a community - to ensure bountiful harvests or continued prosperity, for example.
I believe that most people subscribe to a mix of both deontological ethics and consequentialism. There are some lines (different for each individual) that we just will not cross - mind control, human sacrifice, the torture of children, etc. no matter the cost or the benefit to be gained. In all other cases, we we would be able to accept a little evil "for the greater good".