I don't think there's a tax angle that automatically makes buying from a private insurance company instead of the exchange a better or worse deal. Thus, I suspect the friend providing this advice is confused. You do have that premium credit to factor into analysis... That's not a tax thing though.
BTW, the correct way to treat health insurance for an S corporation shareholder employee is as W-2 wages. E.g., if someone pays themselves a base salary of (say) $50K but also provides (say) $20K of health insurance, the correct W-2 shows the box 1 wages as $70K. Box 3 and 5 shows $50K though so you only pay payroll taxes on the $50K. Then, on the shareholder-employee's 1040 return, and assuming the $20K of health insurance qualifies as a self-employed health insurance deduction, you deduct the $20K from your total income to get to your AGI.
If you have a decent payroll solution, like Gusto, they should do this for you.
P.S. Possibly the friend is probably actually referring obliquely to this wrinkle?