No, actually, you have it backwards.
This isn't going to look pretty, since I can't paste in a table, but this is directly from the Medicare site (see below). Note that the non-facility price is listed first, the facility price second. The rough averages I quoted were simply from scanning the table. If you want to total them up and divide by 91, please feel free. 😉
Note also that CPT 44388 is for colonoscopy by itself. If you search on additional CPT codes, such as 44392 (colonoscopy with polypectomy), you'll find that the prices are slightly higher for more complex codes.
As for private insurance paying more, that's certainly the case with a lot of payors, but perhaps not with others. At any rate, these figures are not readily available, unlike Medicare fees.
Clinicians would be well-advised to conduct a thorough cost-benefit analysis, including malpractice expenses, before taking on any additional procedures. Fees are only one variable in the equation.