His point was this: in the quantum field theories we know, to get correct answers you have to assume all physical processes consistent with fundamental principles do happen. He therefore said (paraphrasing) "since string theory is consistent with the fundamental laws we know, so we should expect it to happen."
Let me elaborate further what he was driving at by discussing three things:
1. The Path Integral: When a particle travels from A to B it exhibits weird "quantum" behavior. Richard Feynmann showed that this can be explained if we assume the particle takes all possible paths from A to B as seen in the above image. In other words, you get the right answer if you assume every possible path a particle can travel it does travel.
2. Feynmann Diagrams: If you want to know how particles interact, again, to get the correct answer you need to assume they interact in every possible way consistent with physics. A convenient way for tracking all possible ways two particles can interact is by drawing Feynmann Diagrams like those on the right.
3. When as physicist wants to derive a relativistic field theory, he/she constructs a Legrangian containing every possible term possible consistent with underlying physics. If he/she does not, then they would not get the right equations of motion.
Okay, back to the speakers point. Because it does not violate any known laws of physics for particles, strings, branes, etc... to exists and be interacting together in some way or another, maybe we should assume they are. We make similar assumptions in 1-3 above, and maybe the remaining issues with physics lie in the fact we aren't including them. In other words, maybe string theoriests are on the right track by including them all; hence we see issues like quantum gravity going away.
Just to be clear, I've never heard this argument before and as far as I can tell it is not the mainstream view. However, it is still an interesting case for string theory.
