Is it true that independent set is $Ω(n^{1−\epsilon})$-inapproximable unless P=NP?
Yes, this is true. 

To see this, notice that cliques and independent sets are complementary. That is, a set of vertices $S$ is independent precisely when $S$ forms a clique in the complement of the graph. Intuitively, this means that if you had an approximation algorithm for finding a maximum clique, you could use it to find a maximum independent set by executing it on the complement graph.