Chiming in late here. Work in HR- have been for many years.
They are not required to provide a copy of his personnel file. They should be required to allow him to review it- he would lose that privledge if he is terminated so I would suggest he does so ASAP.
For any formal write-ups he should have been provided a copy. Also, he should have been able to provide a rebuttal statement if he did not agree with the write up.
In terms of the Comp case, sorry to say it but you would not beleive how many people scam when it comes to these cases. Employers have to be agressive when it comes to assuring that the cases are genuine. The case should have been managed by the carrier and the only time I would call a Dr. is to have paperwork resent if I did not have it for the file.
In terms of how your H was treated when he was out due to a death in the family, don't compare. The person who was off for two weeks may have requested a leave, been granted PTO for that timeframe or time without pay. His company may (should) have a berevement policy. It would typically be in the Employee Handbook if there is one. Have him find that and see if he was outside of the bounds of the policy or not.
I am sure I do not have all the information but I do not see a hostile work environment based on what you have in this post.
Finally, if he is asked to do the work for company Y but in the exact same way with the same parameters and expectations it would be tough for company Y to leagally ( by IRS regs) call him and IC. Just something for you to be aware or.
Best of luck!