Approximation Algorithm for Independet Set Problem: Any Explanation Please?
In general, the maximal degree in a graph can be as large as $n-1$. Therefore on general graphs, the greedy algorithm is only guaranteed to give a $1/n$ approximation, which you can also obtain by returning an arbitrary vertex.

What Corollary 3 does imply is that the graphs that Håstad uses have maximal degree $\Omega(n^{1-\epsilon})$.