Sorry Alex we're going to go to the mats over this one.
The theory is that water at the equator on Mars would have to be kilometers deep (below the surface) to have survived over geological time. This is a deeply engrained belief among Mars scientists and will not be easily dislodged.
But it is important to keep in mind that this theory is based on the *assumption* that the water that evaporates or sublimes there would not be replenished. However there are some theories that explain how this water would be replenished. as for example Clifford's theory. Another possibility is that a combination of favorable obliquity, perihelion, and eccentricity would be sufficient to allow open water pools and perhaps seas on Mars. This could have allowed water to remain at the equator during these favorable periods.

Bob Clark