I can see very few similarities between these two campaigns besides three very common words, "This", "Is", and "Our".... and they don't even caps lock the "OUR" like us (which, although on the surface seems minor, it's really a defining characteristic of our slogan). "This is our time" is a very generic, common phrase (as DS pointed out). It's equivalent to "Let's do this" or "Here we go". It's been used many times before... as opposed to "This is OUR State". Also, of course.... "State" and "Time" imply totally different ideas.
As for the ludicrous idea that our marketing team, even possibly, derived our slogan from this... I guess that's technically a true statement, but I guess it's also possible that God himself handed the slogan to our AD atop Mount Sinai. A much more probably scenario is that we derived our slogan from "This is our house", which is common in sports, and conveys the same territorial idea of our current slogan.