Characters with zero/negative trust are actually the reason the third option exists, since as you've noticed, the other two don't really work. It does mean that there will probably be fewer instances of low-trust people helping each other, but the relative power of the 3rd option helps compensate.
If you find it doesn't work out that way, you can certainly try things out with a minimum bonus of +1, though this means there's not really any difference between Trust 0 and Trust +1.
I also briefly considered changing Trust to go from 0 to 4 instead (and move the 'negative trust' penalty to 0) but overall things seemed to work well as-is. The place it feels like it would sting the most is in shorter games, and for those it's probably a good idea to use the reduced cost to increase Trust from page 60.
All that said, the Trust/aid cycle isn't a tightly balanced equation where everything falls apart if it doesn't work 'exactly so' so if you'd like to give lower trust characters more options, by all means, go for it.