I don't claim that it's true, but here's one more explanation, this one in favor of salt making water boil faster: http://www.swri.org/10light/water.htm
Briefly, they say that salt has lower heat capacity than water, and so water+salt will heat up more quickly than water alone. This overshadows the tiny increase in boiling point that the salt will also cause.
On the other hand, that same site says that adding salt to water will increase its volume, where I think the opposite is true (not 100% sure on that one).
Aside: It's fun how such an easy-to-evaluate experiment has so many different opinions, even with regard to the outcome of the experiment, let alone the explanation (:
Here's someone's video of doing the experiment (the water did boil faster with salt): https://www.youtube.com/watch?v=qcrDuc-XjRQ
Of course, you can poke plenty of holes in their methodology. We need a large government-funded study!
Here is one more link relating to the specific heat of water, when substances are dissolved in it: physics.stackexchange.comphysics.stackexchange.com There, they did an experiment on cooling water, and found that water+salt cools faster. I think it's reasonable to believe that it heats faster, too.