No, no, no, no.
Increasing fresh water may indeed affect the climate of the entire world, but that is because the water column is becoming more stably stratified as the salinity decreases, suppressing overturning. Somehow the deep circulation has to respond to this. In my opinion no ocean model and no oceanographic theory is really strong enough to predict how, or what effects that will have on climate.
But that qualitative uncertainty, which colloquially may be considered “unstable”, traces back to an increase in the stability of ocean stratification in the Arctic.
Get it? Less salty at the surface = more stably stratified. The word “stable” does not appear in the article in any sense. It’s just another bad copy editor headline.
Does this matter? To the editor, to most of the readers, no. Probably nobody will bother trying to get a letter published about this.
To those interested in science, yes. It makes things hard to understand when a word is used to mean the opposite of its technical meaning. To the press, yes as well, because the scientists interviewed will come away with a bad experience and lots of unnecessary explaining to do, adding to their reluctance to talk to the press.