It is not accurate to say that there is "no such thing as privacy, or a right to privacy, when you're connected to a company network or service."
It is true that installing a company MobileIron MDM policy on a personal device does limit privacy, both legally and practically. However, even when using personal device to connect to company services on a company network, it is usually possible to keep personal emails, text messages, and web activity private.
The extent to which the company has the right to review an employee’s personal data depends on a number of factors (e.g., the type of data in question, whether the company owns the device on which the data is stored, whether the data is related to the employee’s job, whether the company has published policies regarding personal data, etc.).
Even if the company has the legal right to store and read and employee’s personal data, it might not be able to. According to MobileIron’s website, a MobileIron MDM policy does allow access to some personal data (GPS location information, installed applications, storage use, phone number), but does not allow the company to access certain types of personal data (personal email, photos, videos, text messages and voicemail, and web activity). In short (if MobileIron is telling the truth) the bulk of the user’s personal information and data remains private.
That said, the company does have the ability (but not necessarily the legal right) to view and record any data that is transmitted using their network. However, if the data is encrypted, it may be practically impossible for the company to read it. Some protocols encrypt data by default (e.g., iMessage, SSL-enabled email protocols like SMTPS, IMAPS and POPS, certain instant messaging protocols) and others can be configured to do so. Encryption does not necessarily ensure privacy, however – for example, the company may prevent end-to-end encryption by requiring that traffic pass through a proxy server, or by blocking certain protocols entirely.