I looked into to it both privately and with the State employment board the year it happened... of the three classes of exemption... Executive, Administrative, Professional... the consensus was my employer had the option to reclassify my position under "Professional Exemption". I realize only a court has the final say... but it was clear that it was not a black and white issue....
This said... Under both federal and state law, employers bear the burden of proving an exemption applies (that the employee is appropriately classified as exempt) and damages, if awarded are generally retroactive for a maximum of 4 years...
For a time, in the 90's, we were part of the Largest Healthcare organization in the country and I received a pink slip on acquisition because corporate policy was to outsource engineering... my boss told corporate any money they think they might save would evaporate the first time a case was cancelled due to a Facility Problem... Corporate backed down and in 1998 completely divested from the California market...
As I stated, I'm not an expert and you have done your home work. There is zero protection for exempt employees under FLSA. I work for a very large university and we have employees including doctors, nurses, mechanical and systems engineers, policeman and tech support on 24/7 call. I'm still surprised by the classification, but this is a very complex area. I'm just about to retire from my job as an internal management consultant, dealing with management issues just like this one. I will offer a couple of suggestions about what I would do if you and your boss were my client.
There are two (actual I see many more) issues here. The first is how can you be contacted at all times (the subject line) and the second is what happens when that isn't possible. I'll start with the hard one, what happens if you can't be there because of illness, accident or a hundred other reasons.
I was the backup to my tech support manager when I was responsible for the unit that provided computer support to executive management. I made sure that my manager had every communications tool available, but I also knew she had a family and a personal life that needed to be respected. I think your boss' expectations are completely unreasonable. My guess is she doesn't have the skills to be your backup. Without you, she is subject to failure and her actions are driven by fear. Not a healthy situation for her, you or the hospital.
Given that neither of you want a failure (a disruption of patient services being a prime example), I would think you need a much better back-up strategy. My guess is that you will need to develop the plan for her. You may already have a list of local companies (HVAC, plumbing, electrical) that you use and trust who could be called in when you aren't available. This doesn't have to be costly and can be managed by you. But you will need to provide her with specific implementation instructions. If you want to PM, I have some ideas on how to approach this. Bottom line is that you both would sleep better if you have a "business continuity plan" in place.
The university, as a general practice, providers workers with the proper tools to do the job. That includes, in some cases, satellite Internet connections and phone service. As others have suggested, I would investigate the best technical solutions and present those to your boss. The trick is to present them as a solution to her problem of how to always be able to contact you. You may need to do a cost/benefit analysis if that is important to her. The bottom line here is that you are going to need to do all the work and planning here too.
The advice is free and that is probably its value, but I do hope you find solutions that make your tractor time more enjoyable.
