Why do rivers have 'wells' in mountains?
The presence of water underground has nothing to do with sea level in mountainous country.

When rain fails on a mountain, or snow falls on a mountain and the snow eventually melts, the water from the rain or snow melt mostly travels downhill via rivers to the sea.

In getting to a river some of the water will fall on the ground. In places where the ground is covered by soil, water can travel through the soil via the pore spaces between the grains of soil. Similarly if porous rock, such as sandstone lies beneath the soil water can travel through the pores in the rock.

If a layer of impervious rock lies under the porous rock or soil, the water cannot move downwards, due to gravity, any further. This can lead to water accumulating in the soil or porous rock and saturating the soil or rock. In such situations an aquifer can form. The top of the saturated zone in an aquifer is called a water table.

The ground beneath a river is saturated and the surface of the river shows the water table exposed to atmosphere. Thus in mountainous regions the ground beneath rivers will be saturated and capable of supporting a well developed from the bank of a river.