The reason we don't need any more clarity in the rules is because of how mage wars defines damage. You only take damage when damage actually gets applied. If you didn't apply any damage tokens or mark it on your status board, then you didn't take any. 0 damage is the same as no damage. Saying that you take damage when you don't take damage makes no sense and shouldn't be something we need to clarify.
So yes you can hit a vine marker with a zero damage attack, but hitting it doesn't destroy it. Dealing damage does. What the rules are saying with "any amount of damage" is that you can't really increase its life above 1, because 1 damage will still kill it. But you still have to do that one damage to it to kill it. Now, if there was a way to give it armor, that could help keep it alive.
I vaguely recall (and am too lazy/busy to look it up right now) that an attack "hits" if it is not avoided in the Avoid Attack step, even if it rolls all blanks or deals no damage (due to armor for example). Has this changed? And while the vine marker rules don't use the term "if the attack hits" but rather "any damage", it's still a little vague, since "any" usually includes "0" as long as an attack "hit".
If you're familiar with X-wing miniatures, it's kind of like how Lt Blount can "hit" even if he doesn't deal damage, and a "hit" can strip a Stealth Device even if no damage is dealt (and a lack of a "hit" won't strip a Stealth Device, even if damage was dealt in some other way), and various other effects trigger on "hit" while others trigger on "damage" and these things are not the same; in fact, several secondary weapons say something like "if this attack hits, cancel all dice and [do something]." Similarly, a "hit" and "damage" are not the same in Mage Wars, and whether or not "any damage" includes 0 or not should be defined somewhere.