Yes, the press have a lot to blame for misunderstanding, and inaccurate and incomplete reporting. Not a new observation, is it ?
If 1000 scientists produce fine work, and 1 produces something dodgy, guess which one appears in the press & gives scientists a bad name ? And, the vast majority of scientists aren't doing headline work, they're just plodding along discovering a single piece of the jigsaw of Life+Universe+Everything.
On this particular issue, the article is about the accelerating contribution to sea levels by polar ice melt. This is just 1/5th of the total sea level increase, most of the rest being caused simply by expansion. The impact of this is slow in human terms, but incredibly fast in nature's timescale. The knock-on effect on sea currents, sea temperature, salinity, ocean cycles, cloud cover, rainfall, extreme weather, etc, etc is near-impossible to predict. However, some predictions are possible - eg, most of Bangladesh will cease to exist in 40 years time (could be 30, or could be 50).
The remaining climate scepticism is now understood - this issue (and global overpopulation) is so far beyond human experience that it's no surprise that many just cannot believe it despite the facts. I've mentioned previously a presentation by a Harvard psychologist on the subject - recommended watching.
Personally, I think overpopulation is an even bigger catastrophe, underpinning just about every major problem on the planet. Sorry, no solution, until nature resolves it in some unpleasant way.