Jeremy, I'm begging you to reconsider purposely staying on the same side of the street with the intent to make eye contact and say,"Hi." Of course, extenuating circumstances prevail, but as a rule, it's wise to be cautious. Ounce of prevention, pound of cure.
I agree with your general idea that people ought be prepared for anything: plan for the worst; hope for the best. Sometimes, if it's obvious to the attacker, stepping across the street inspires the chase too though. Sometimes though, it's stupid not to find a quick change in route. When I worked nights in an alley frequented by crack-heads and very very cheap prostitutes (and their pimps), I always looked them in the eye and smiled or gave a respectful nod, depending. But as you can likely attest, with some folks, it's better not to engage in any way.