This is often cited but there's not much precedent to support that the Rules give you carte blanche.Portable HAM (you don't need a license to transmit in an emergency)
First is that the FCC gives a licensed amateur leeway to use whatever means necessary to protect life or property. This doesn't give just anyone a free hand to operate without a license. I'm not aware of a general rule that allows anyone, anytime to operate. There may be, I just don't know it. The Part 97 presumption is you're already a licensed station and you need to use privileges beyond your license. For example you're just a Technician and want to use voice on 40m where you'd normally need to be General or Extra class. It may imply that your ham ticket gives you authority to operate beyond the Amateur Service but it does not say that explicitly.
Second the understood need is that you have no other means but carrying an InReach would indicate otherwise.
If you choose to invoke the safety and distress authorization that you should be ready to expect a fine, so make it worth it. The FCC won't care that you didn't bother upgrading your ticket or getting the appropriate license. The best case is probably that they don't revoke your ham license and just give you a warning.
§ 97.403 Safety of life and protection of property.
No provision of these rules prevents the use by an amateur station of any means of radiocommunication at its disposal to provide essential communication needs in connection with the immediate safety of human life and immediate protection of property when normal communication systems are not available.
§ 97.405 Station in distress.
(a) No provision of these rules prevents the use by an amateur station in distress of any means at its disposal to attract attention, make known its condition and location, and obtain assistance.
(b) No provision of these rules prevents the use by a station, in the exceptional circumstances described in paragraph (a) of this section, of any means of radiocommunications at its disposal to assist a station in distress.