Anyway, I'm no academic, so here's the practical stuff.
Safety language is a way to vocalize that you are currently thinking critically about something. It is the verbal suspension of certainty. Communicating in this manner shows that you have separated an observation from an inference or judgement about that observation. It is a precise statement that says you do not currently know and need more evidence.
Think about the difference between these two phrases.
It is going to rain today.
It looks like it might rain today.
To me, the different modal verbs show distinctly different stages of critical thinking. Namely, certainty and uncertainty or suspension or certainty. These examples are pretty simple but they can be applied to observations made when testing software. When performing black box testing, you have a fairly limited scope of what you can observe. You have the UI you are interacting with and possibly some log files and a database (though that may not longer be black box testing at that point...?). At any rate, you are not looking at the code so your understanding of what it actually happening is limited.
Due to the lack of knowledge about what is really happening, when communicating observations it may be wise to be precise about what you do not know. Love to hear your thoughts and experiences in using safety language.
This is soloist Demondrae Thurman playing Slavish Fantasie.