Yea, this letter could have been written about garden variety "suspected cheating" 20 years ago. And the professor's attitude is the same as a couple of professors I remember back then:

Prof: "I know you cheated."

Student: "How do you know it, can you prove it?"

Prof: "I have ways, trust me I know."

Student: "I know the material, I'll re-take the test right in front of you if you want."

Prof: "Either admit that you cheated and get a F, or don't admit and I'll send you to the school's academic integrity department."