The biggest question nobody is asking is why hold that press conference, and specifically when they did and not before? Who does it benefit? That question has to be considered knowing that in reality the appeal process is now over, she has been found guilty and she is banned for four years. Why wait until now to try to convince everyone she's innocent? Yes, technically they can appeal to the Swiss Supreme Court, but only on very limited grounds. The grounds are;
1.) the tribunal was not properly constituted;
2.) the tribunal wrongly accepted or rejected jurisdiction;
3.) the tribunal ruled beyond the claims submitted or failed to decide one or more claims;
4.) the parties fundamental procedural rights were breached; or
5.) the award is incompatible with public policy.
They had their lawyer speak first. He did not, nor did anybody else, address any ground of appeal which would now be the only relevant matter to discuss. Clearly they were not there to discuss that, the purpose of that was PR and PR only. It was to get out there first, spin a story that despite SH being found guilty of doping, convince as many people as possible that the decision was wrong or could be wrong. To create doubt and make people not trust the process.
The point being that the press conference wasn't really for SH - it wasn't going to and can't change anything for her. She's banned for 4 years, that's done. Why then is it important for people to believe she was wrongly convicted ? Who does it help now?