Personally, if my employer feels I need access to email or to be reached 24/7, it is their responsibility to provide the means for that. They do not have the right to takeover my personal property or data just because I work there. Put differently, if there is a business reason for them needing me to receive emails/texts/calls outside of normal working hours, then they should provide a business solution. If I want to do it for my own convenience on my own device, well, then I would have to weigh the convenience against all the privacy issues involved.
This. I just tried to argue this same point where I work; I work in an IT group that has a rotating 24x7 on call. We had employer-issued Blackberries, which both received SMS messages and could connect to email. Since we had had them for a while, the SMS alerts over time had evolved to "X has failed. Check your email for details." Then the company forced us to turn in our Blackberries and went to a BYOD. I tried, unsuccessfully, to argue your point. I get spotty coverage on my personal phone, and none in the building, so that would rule out my personal device. Plus I refuse to allow the company control of my device, stipend or no. The alternative was to accept a "penny phone" (a Samsung Chronos 2). I was very clear with my boss and boss' boss what that could mean for response to pages. So far, nothing has come up, but I also am kind of heistant to stray far from home when I am on call.
In case of atomic attack, all work rules will be temporarily suspended.