I seem to remember a conversation somewhere about this where it was stated that the intended meaning was that the Corp always had at least one bad publicity (through Lukas tweeting or Jakodrako’s inside information or something).
I would maintain that the actual meaning as written on the card must be that bad publicity can be removed down to zero while the current is in play or else you prevent bad publicity being removed at all. The simplest way to describe why would be to say that as the rule says:
“The Corp has 1 additional bad publicity (even if they have 0).”
one might equally validly rewrite that as:
“The Corp has 1 additional bad publicity (even if they have 3).”
or 7, or 13, or whatever number you choose, since the “even if” clause doesn’t note anything special about zero but just specifically includes it in the set of values of bad publicity for which the additional bad publicity will occur. Other values of bad publicity are already implicitly assumed to trigger the additional effect.
So that if the act of removing a bad publicity down to zero was ruled to result in the Corp gaining an additional bad publicity to have one again (whether that is classified as a constant effect, triggered effect or whatever) because “The Corp has 1 additional bad publicity (even if they have 0).” then it would stand to reason that the act of removing a bad publicity down to three must also result in the Corp gaining an additional bad publicity to have four again, since “The Corp has 1 additional bad publicity (even if they have 3).” is just as valid a statement.
The way it is currently worded there is nothing special about the number zero, rather it is simply included on an equal footing with all the rest of the possible bad publicity values and should therefore function the same.