It has nothing to do with the law. It has to do with an "at will" employment contract. The employee and employer have the right to terminate employment for any reason or no reason. In this case, the company made a no smoking policy and set a "drop dead" date for compliance. They provided a means to comply. This employee chose not to comply. He violated his employee contract. The company is completely within their contractual rights.
I work with an "at will" contract. It's been that way for 30 years. Both states where I've been employed are also "right to work" states. I can't be forced to join a union as a prerequisite to be employed. Freedom and responsibility. I'm not obligated to remain with my employer if I choose to leave either. Some people "owe" the company for "training". They aren't free to leave without compensating the company or "working it off". That was a common occurrence for employees of Electronic Data Systems.
"Any" reason isn't exactly correct, because "certain" reasons (race, religion, etc.) are protected. Otherwise, your post is spot on. You're better off as an employer to give "no" reason for employment termination to protect yourself from federal/state laws.