Our organization is covered by FMLA, and our employee is eligible. The problem is this: he has a heart condition that requires intermittent short in-patient hospitalizations for treatment, which clearly falls under the FMLA. He doesn't want to count the leave time for heart treatments as intermittent leave under the FMLA, however, because he has upcoming back surgery scheduled and wants to have all of his FMLA time (12 weeks) available. Is he allowed to decide whether his leave for the heart treatments is FMLA or not?

From what you have related, the employee has a serious health condition (heart-related and requiring multiple intermittent, in patient treatments) under the FMLA. 
Under the FMLA regulations, you, as the employer, are required to designate the leave as FMLA leave, even if the employee does not want you to do so.

Nothing prevents you from offering additional leave in your handbook of policies and procedures.

Jack McCalmon, Leslie Zieren, and Emily Brodzinski are attorneys with more than 50 years combined experience assisting employers in lowering their risk, including answering questions, like the one above, through the McCalmon Group's Best Practices Help Line. The Best Practice Help Line is a service of The McCalmon Group, Inc. Your organization may have access to The Best Practice Help Line or a similar service from another provider at no cost to you or at a discount. For questions about The Best Practice Help Line or what similar services are available to you via this Platform, call 888.712.7667.

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