While the 22 Hornet is certainly not reccommended as the ideal, or even minimum, deer rifle, it probably has accounted for a lot of deer. If the hunter is a careful shot at 100 yards or less, a head shot will drop a deer. I would suggest a heavier caliber for deer such as a 243 Winchester. It doesn't have a stiff recoil for an inexperianced shooter and is much more effective at a longer range. Fit it with a moderate power scope and you have a very good rifle.
I take exception to the statement that shotgun slugs are "slow and low powered". At reasonable range, the moderen 12 gauge sabot is an accurate and effective deer killer. A 385 grain slug at 1900 ft/sec is not something I'd want to reach out and catch, although they will put 3 shots into a target the size of your palm.