It is hard to imagine an 'earth-like' planet, with 'earth-like' oceans, that did not have active plate-tectonics, or plate-tectonics in the past. Although small amounts of water exist on Mercury, our Moon, and Mars, these do not now have oceans or an atmosphere anything like the earth's atmosphere. Earth is the only planet (anywhere) we know for certain has continents, ocean-basins filled with liquid water, and an atmosphere of water rain and snow - the Earth is also the only planet (anywhere) we know for certain has active plate-tectonics and has life.
I think the statement you cite is true- as a description of expert opinion - many planetologists would agree that plate-tectonics plays an important part in maintaining water on a planet's surface. A planet that had oceans, but never had plate-tectonics, would be very different than the earth. That does not mean such a thing can't exist, it just means it would be quite different from our current experience with planets.
Most of the liquid water on the surface of the earth fills the ocean basins. We understand the ocean basins (on earth) as having been formed by the process of plate-tectonics. Plate-tectonics is required to generate ocean crust as we know it.
Plate-tectonics implies active convection is taking place in the planet's interior (at least the mantle). Less directly, it implies the planet's interior is dynamic, and may have active convection in a metallic core which might support a magnetic field. The earth's magnetic field has probably protected the earth's atmosphere from being blasted away by the solar wind. (The possible fate of Mar's atmosphere and oceans.)
The chemical component H2O plays an important part in igneous petrology. Water containing minerals recycled back into the earth at oceanic trenches (subduction zones) can lower the partial melting temperature of the mantle, may lower the effective viscosity of the mantle, and may be required for the formation of continental crust.
Submarine hydrothermal systems, located along the mid-ocean ridge, alter the chemical composition of the ocean. Life may have first originated in these hydrothermal systems, which exist due to plate-tectonics.
Surface water on the earth may have had an extraterrestrial origin or may have outgassed from the planet's interior (likely both over the course of history.) Volcanic gasses contain much H2O and CO2, and the outgassing of volcanic gas during plate-tectonics may have been an important source of surface water on earth.
No one really knows for certain whether an exoplanet will be discovered that has oceans without plate-tectonics, or even plate-tectonics without oceans. The article you cite (and others I've seen also) should perhaps be taken to mean that plate-tectonics is currently the paradigm by which we understand how an earth-like planet works. It would be very interesting for planetary science if something different were found.