Earlier quoted context omitted.
On the contrary - there's a few things they can do. They could examine the difference in results between the two tests at the individual-student level, for example. Or, using the set of students who admit to their cheating as a training set, do a question-level analysis.
Doesn't prove anything. Sometimes you don't get enough sleep and do poorly on a test. Sometimes you just have a great day. Using statistics as though they are hard facts and not merely suggestions of likelihood is a terrible idea when there is a question of guilt or innocence. I have in the past had wildly fluctuating grades. Don't believe everything your powerpoint-prettied software stats tell you.
This actually happened when I was studying engineering at Waterloo. The course was calculus 3 and the prof, who normally taught math majors, didn't know that there was a university commissioned exam bank with previous exams for courses. Course coverage was sporadic for all but final exams, so we normally didn't check it, but the previous midterm was actually there. One of us found it 24 hours before the midterm, so half of us got it and half of us didn't. The prof had reused the hardest question. Long story short, nobody got in trouble, but the prof made it so your top and bottom "midterm" (there were 5 of them before the final) could be optional dropped together or not at all.