How do some plants grow in salt water, while others die?
A few things you have to realize when you ask 'why hasn't species x evolved trait y':


What is the cost of evolving this trait? If you gain one trait, you lose another (or others). Everything in evolution is a tradeoff: that's why you're not nine feet tall, you'd be able to beat up all your enemies great, but it would take so much food to sustain you, it wouldn't be worth it.
Not every trait can be easily evolved. When you're starting as a freshwater plant, there are many, many, many, many mutations that have to occur for you to become salt-tolerant. Every one of those mutations would have to give a fitness advantage to be positively selected. The chances of this happening are low, which means if it happens at all, it would take a long time.
Who knows, perhaps these plants are, slowly, becoming more and more salt-tolerant and you're seeing them at an intermediate point in their evolution. Everything is evolving all the time, if these plants were not in a salty environment until recently, mutation and selection haven't had time to work their magic.


Update from comment:


  Can you flesh out a little on "How can the plants keep from intaking salt, while absorbing other soluble nutrients through the roots?"


Sure! I'll give you the simple answer first: there are different mechanisms for absorbing salt and for absorbing nutrients, so they can function largely independently.

Now the longer explanation: Salt and nutrients don't just diffuse (much) through cell walls, they have to be transported across by what are called transmembrane proteins. Think of the cell membrane (a layer inside the cell wall) as basically something like a layer of oil (it's called a lipid bilayer) -- you know oil and water don't mut, and for the different ions in salt (sodium ion and chloride), neither do oil and salt or oil and many nutrients so they get sort of escorted across that barrier by big proteins that form sort of a tunnel through it.

There's a different transport protein for different substances; the salt ones will only let salt through, and in fact there are different ones for letting salts in and letting salts out, and for the different ions (sodium and chloride) in salt.

Update from comment:


  This makes me wonder how salt harms most plants, if it can't get in except by 'invitation'


Quite a bit of salt can diffuse in, the molecules are small enough (unlike most nutrients) to pass through the membrane via the channels that let water in. Every living creature has a quite sophisticated setup of "ion channels" to pump salt out. If suddenly its cells are in a very salty environment, these pumps can't keep up.

Update from comment:


  So if salt can diffuse in, what do salt-tolerant plants have that other plants don't?


Mostly, if I recall correctly, three things: They will have enzymes that have evolved to work in higher salt concentrations, they will have cellular functions to "sequestrate" salt, i.e. store it in organelles called vacuoles instead of leaving it where it can harm other organelles, and of course they will expend more resources on ion pumps to get the salt concentration in the cell to an acceptable level.