The purpose of the letter is to avoid the unemployment hearing -- the strength and length of it is to deter the bosses flat out first hand ... a sorta make them pee their pants move.
I don't think this letter is going to impress anyone's employer, and will probably lead to the employee's termination. The letter is filled with street-lawyer nonsense. In particular, most of the second paragraph (discussing the ADA), and all of the third and fourth paragraphs are wrong. An employer may ask questions and request documentation to determine whether an employee has a "disability" or to determine whether that disability necessitates an accommodation under the ADA. The FMLA does not prohibit an employer from requesting medical documentation, and in fact explicitly allows an employer to require certification from a health care provider before granting medical leave. HIPAA does not apply to employers. Requesting proof of vaccination does not meet the elements of any of the four forms of the invasion of privacy tort, nor does it meet the elements of battery. Requiring an employee to be vaccinated certainly does not constitute battery.
The strongest argument would be for a religious exemption, but the rest of the letter undermines that argument by revealing that the religious exemption is probably insincere.