The article on the front page and the comments by Greg Harger are all focused on the procedure in the USATF's Competition Rules. That's not the whole story.
In addition to the Competition Rules, you need to look at the USATF's Bylaws. Because the USATF is the governing body for track under the USOC, it has to provide procedures to protect athletes in the selection process for international competitions (like World Indoors). Here's the relevant part of the Bylaws:
OPPORTUNITY TO PARTICIPATE IN CERTAIN INTERNATIONAL ATHLETIC COMPETITIONS
A. Opportunity to participate: USATF, its Associations and sports organizations recognized by USATF may not deny or threaten to deny any athlete, coach, trainer and other medical support staff, manager, administrator, or official the opportunity to participate in the Olympic Games, the Pan American Games, world championship competition, or other protected competitions defined in the USOC Constitution, nor may USATF, its Associations, or sports organization members, subsequent to those competitions, censure or otherwise penalize (1) any person who participates in those competitions, or (2) any organization that the person represents. USATF shall, by all lawful means at its disposal, protect the right of a person representing the United States in any of those competitions. Any athlete, coach, trainer, manager, administrator, or official who alleges that he or she has been denied an opportunity to participate in Athletics competition shall be entitled to fair notice and opportunity for a hearing under Article 14 and Regulation 21.
B. Investigations: Any athlete, coach, trainer, manager, administrator, or official who alleges that he or she has been denied by an Association or sports organization a right established in paragraph A above shall immediately inform the CEO, who shall cause an investigation to be made and steps to be taken to settle the controversy without delay. If the CEO is unable to settle the controversy, he or she shall refer the matter promptly to the CEO of the USOC for action under Article 9 of the USOC Constitution. By maintaining membership in USATF, each recognized Association and sports organization agrees to the process in this article.
Regulation 21 goes through the arbitration procedure and covers allegations that "a party has violated USATF’s Bylaws or Operating Regulations, USATF policies, or the Sports Act; has violated the IAAF eligibility rules; or has engaged in conduct detrimental to the best interests of Athletics or USATF." It also provides for mediation where the parties can settle their dispute.
USATF is also subject to the USOC's rules and there is also an arbitration procedure under Article 9 of the USOC's Bylaws that appears to apply to athlete selection for international competition.
In this case, GG was reinstated after her agent, and presumably her lawyer, had filed for or were getting ready to file for arbitration. I assume they were going to allege that the USATF violated its own rules by disqualifying Grunewald after not following the USATF's own procedures and not having "new conclusive evidence." If an arbitration panel had found that GG was denied a spot in international competition in violation of the USATF's own rules, I assume the panel could have ordered her to be reinstated.
Instead, Max Siegel, as he is required to try to do under the USATF's Bylaws, reached a settlement with the agreement of the affected parties (GG and Hasay). This all appears to be permitted by the USATF's Bylaws.
It looks to me like the bottom line is that when it involves selection for international competition, there is also a higher level than the Jury of Appeals, which is the arbitration process under the USATF's Bylaws. Once you are starting the process under the Bylaws, it's permitted and encouraged to try to settle the dispute.
I almost hate to be defending the USATF since they are generally so incompetent but it looks like they were right in reinstating GG in this case. Maybe the incompetence is in not explaining the Bylaws procedure and trying to sweep things under the rug yet again.
I would be interested if there are any sports lawyers out there who have an opinion or experience with the subject.