There are really two issues in this case. In my view, there should be a third.
The first is whether or not this was a constitutionally justified search. The Court will consider "whether the action was justified at its inception" and "whether the search as actually conducted ‘was reasonably related in scope to the circumstances which justified the interference in the first place." To make these determinations, it will have to decide whether "the measures adopted are reasonably related to the objectives of the search and not excessively intrusive in light of the age and sex of the student and the nature of the infraction." Stafford v. Redding, 531 F.3d 1071, citing New Jersey v. T.L.O., 469 U.S. 325.
It think it would be hard for them to draft an opinion arguing that strip searching a minor with no prior disciplinary problems, solely on the word of another student, in search of ibuprofen, is not "excessively intrusive in light of the age of the student.. and the nature of the infraction"
The second question is whether the school officials are entitled to immunity from lawsuits by the student, because the state of the law was too unclear for them to be on notice that their actions were illegal. The lower court held essentially, that although there was no case expressly forbidding this conduct, its so clearly contrary to common sense and decency that they should have known. I agree with this view, but think there's a fair chance that the Supreme Court will not, largely because there are some bad court decisions out there they can point to as creating ambiguity in this regard.
I also think that there is an issue that is overlooked here, which is the fact that this is not merely a "search" it is the infliction of a trauma on a minor. I'm not aware of there being any legal support for this, but I believe in general that a "search" that causes greater harm than the offense its seeking to uncover should be considered cruel and unusual punishment. I think few would argue that catching a student with advil would justify ordering the student to be stripped as a form of punishment through humiliation.