"Bind" vs. "bond"
Solution 1:
The way I understand this idiom is that the two nouns bind and bond are contrasted, not the two verbs bind and bond.
A bind in this sense is the object that ties things together. A bond is the result - that two things are tied together. So this idiom is saying that we don't end up trusting each other because of how we are tied together, or what brought us together; rather that we trust each other because of the bond that formed between us - the closeness that we have for one another because of being somehow tied together.