The answer to the question is yes, there are limits. I'll expand for ICAO regulated airports, but this is also true for FAA ones.
ICAO defines an area surrounding a runway, called runway strip, which purpose is to:
a) to reduce the risk of damage to aircraft running off a runway; and
b) to protect aircraft flying over it during take-off or landing operations.
A water runway strip would not reduce the risk of damage to aircraft running off a runway. It would in fact increase it, so a runway strip cannot be made of water.
The size of the runway strip depends on the type of runway, but it ranges 150 m to 0m (zero) in width, and it must extend 30 to 60 m beyond each end of the runway (or the end of the stopways, if there are any).
So, the runway strip contains at least the runway (and its stopways) and extends beyond it on its ends, and sometimes (depending on the type of runway) it also extends to the sides of the runway, and it defines the limits to how close a runway can be to water.
Going even further, ICAO defines a Runway End Safety Area (RESA) for some types of runways which further increases the minimum distance of water to the runway.
Airports such as Sint Marteen, where the runway is almost 190m from the water, are just examples of how the runway strip and the RESA are applied as safety measures against aircraft running off a runway.