I do not think we are unique but I believe we "human like intelligences" are a very unlikely product of as many tiny random adaptations as to make the number of rocky planets in the observable universe look like a small number.
This is how I look at it: the Earth is an ecosystem with millions of species that's been evolving together for billions of years, adapting to each others changes as much as to the change in climate etc. The combinatoric is huge, but some environmental pressure make that process invent over and over similar solutions to the same class of issues. Some traits are totally random and I believe will exist only once in the whole history of the universe, and some traits are heavily constrained by environment/chemistry and are invented over and over by evolution, on Earth and elsewhere. Is intelligence of the former or later class of traits?
Some organ to predict the future is certainly part of the heavily constrained invention. But I can't convince myself that a human like intelligence able to escape Earth, both in imagination and in practice, is anything more than a fluke. I just don't see how to logically connect super-intelligence with how evolution works.
On a higher level, your idea also evokes a whole set of similar ideas that are all based on multiplying tiny chances of high intelligence with sextillions of planets, such as "life is a simulation" or "matrix like brain in a jar". My intuition tells me that we can't extrapolate that far without the unknown dominating everything.