"A chronometer watch is a specific type of watch tested and certified to meet certain precision standards. In Switzerland, only timepieces certified by the COSC may use the word 'Chronometer' on them".
There are other types of chronometers (or used to exist, before atomic clocks and GPS) but, as you stated, they are tools and not watches.
So, IMHO, a chronometer has nothing to do with the ability to hack or not, but, again IMHO, a chronometer wrist watch that does not hack is painful to be properly set.
That is the main reason that most of precision freaks, like me, prefer watches that hack but this is a pure preference. I like the Zenith El Primero movements and they don't hack.
On a summary, the non-hacking ones are just a little more annoying to be set.
An ideal watch for me (that does not exist, as far I know) should be one that when you pull the crown to adjust the time, when you press the crown back the seconds should reset to zero and then keep going.
About your example, there is an extreme one that says that a stopped watch is perfectly correct twice a day.
Cheers,
Nilo