Curious what happened here, Citation goes missed. That would be a hint for me. The IAP shows circling minimums at 600. Situations like these are unfortunate.
While the Citation going missed might be a hint that the weather is below minimums, a proficient Part 91 IFR pilot should not theoretically have a problem flying an approach to take a look as well; that is unless fuel is approaching reserves.
Consider this: During instrument training just about every instrument approach an instrument candidate flies is to the minimums (DH or the MDA, depending). Other than fuel and proficiency, there should be no reason why a Part 91 pilot should not be able to fly any approach to minimums thereafter, if for no other reason that to have the opportunity to practice it and practice the transition to the missed segment (which arguably is perhaps the most challenging part of flying on instruments).