You can waste your time and effort appealing to them but don't be surprised when it is rejected. You can also then appeal to the IAS and, again, don't be surprised when that is rejected.
The points that you mention are all valid. However, I can tell you from experience that they will not make a difference until this is challenged in court. They will, eventually issue a claim and that is good, because you will be able to put the points before the only truly independent arbiter, a judge. But then again, as long as a claim is defined with our advice, it will never get as far as a hearing as it is more likely than not going to either be struck out or discontinued.
So, fire away with an appeal if you want. It's your time and effort.