I would think employers are free to use whatever hiring standards they deem fit so long as it doesn't violate the big no-no's (Race, gender, religion, age, etc).
Apart from doing it sneakily as you suggest is quite possible, quite a few states have enacted protective legislation, preventing overt employment discrimination against smokers.
"As of 1997 there are 29 states that legally prohibit employers from hiring/firing employees due to their off-work smoking status. They are: Maine, New Hampshire, Connecticut, Rhode Island, New York, New Jersey, West Virginia, Virginia, North Carolina, South Carolina, Louisiana, Mississippi, Tennessee, Kentucky, Indiana, Illinois, Wisconsin, Minnesota, Missouri, Oklahoma, South Dakota, North Dakota, Wyoming, Colorado, New Mexico, Arizona, Nevada, Oregon and Montana.
The District of Columbia and the city of Boston have enacted legislation which prohibits employment discrimination against smokers.
In ANY state not on that list, employers can choose not to hire smokers--or not to hire non-smokers--if they want to. If the boss is a smoker, he or she could just as easily choose to hire only smokers for jobs in his/her company. It cuts both ways. Only job discrimination based on ethnic background, religion, political party, age, gender (and sometimes sexual preference) is prohibited in all states. Smokers are NOT a protected class with regard to jobs unless there is specific state legislation that protects them."
The Smoker's Club, Inc. Encyclopedia 2
Note that Tennnessee is listed in the above as having protective legislation. I have not checked the Tennessee statutes to verify, but
if it does still have such legislation on its books, then perhaps this hospital will not be allowed to carry out its plan.
I do know that the Town of Amherst, NY's desire to do the same was recently scotched, precisely because it would have been illegal to discriminate in hiring against smokers under NY law. The news coverage about that was posted right here on ECF:
http://www.e-cigarette-forum.com/forum/law-e-cigarette/55618-amherst-hiring-plan-goes-up-smoke.html