For state flagship universities as I have said in an earlier post, selectivity is directly correlated with population, and like @coloradomama says, you can get a great education in some areas at CU. IMO most elite institutions are sub 10% and correlate with the top 20 universities (BTW no publics meet that criteria for elite), however if you look at specific majors you will find top 20 programs within many public universities. For CU here are a few of them. and they are right there among the “elite” universities (including private universities).
Smead Aerospace: No. 8 public, No. 11 overall
Environmental engineering: No. 7 public, No. 11 overall
Chemical engineering: No. 11 public, No. 17 overall
So, no, CU is not an overall elite university (IMO no publics meet that criteria) but it definitely has some elite programs within the university. Now if you want to compare apples to apples, and eliminate privates from the conversation then for CU you would still have the same argument, not an elite public university, but definitely has many elite programs within.