IN both situation I think the car owner/renter should push for retail value plus substitute transportaiton.
She was provided with substitute transportation for a period of time, my guess is the substitute transportation was terminated after the claim was settled (albeit not to the individuals satisfaction), but the article leaves out the full time line. Or the claim exceeded 30 days, and that was the maximum coverage her policy afforded her if she self claimed (which it sounds like she did considering her insurance company paid for the claim). Again, the article doesn't say how long she was provided a vehicle just that it wasn't enough time for her to find a new one. That leads me to believe that she is complaining because she may have taken her time to find a car, and it exceeded reasonable expectations (30 days is usually considered sufficient when it comes to insurance claims).
As for the amount she was paid, she was paid a retail value of what a replacement vehicle would cost in pre-accident condition. Assuming this happened recently, a 2003 Honda Oddysey in Average condition (sorry, I doubt "very good" is the same as excellent condition, and even "very good" is arbitrary without seeing the actual analysis report) with 120,000 miles would be worth right on par with what she was paid, in terms of retail value.
In the end, I think she got what she should have received, she got paid for an amount that would be reasonable to replace her vehicle with a like vehicle and she was provided transportation for a reasonable time frame (probably 3 - 4 weeks). Accidents happen, and that is why we have things like insurance, but we shouldn't expect to "make" money on an accident, we should only expect to be made reasonably whole.
On a side note, I like Chris Elliott, he usually puts a voice of reason into travel issues, but he really should stick with travel issues and stay out of offering insurance advice for what companies should do or what is or is not reasonable without providing facts to support his broad based opinion.