The term "supposings" is found within the teachings of other Thai Ajahns as well. In the cases I have, Ven. Thanissaro has translated each one. They are making a crucial point with this term.
In The Craft of the Heart by Ajahn Lee
sammati: In Thai, the primary meaning of this word is “supposing,” which is
how it is translated here, but it also conveys the meaning of convention (i.e.,
usages which are commonly designated or agreed upon), make-believe, and
conjuring into being with the mind.
example from the text (there are several)
We don’t understand the states
of mind that have been supposed into being, and so don’t see the mind that is
released from supposing.
So it is with the heart when the expert craftsman, discernment, has finished
training it: We call it nibbana. We don’t call it by its old name. When we no longer
call it the “heart,” some people think that the heart vanishes, but actually it’s
simply the primal heart that we call nibbana. Or, again it’s simply the heart
released, untouched by supposing.
http://www.accesstoinsight.org/lib/thai ... _sure.html
All the things in the world are suppositions that we've supposed into being. Once we've supposed them, we fall for our own supposings, so nobody lets them go. They turn into views and pride, into attachment. This attachment is something that never ends. It's an affair of samsara that flows without respite, with no way of coming to closure. But if we really know our suppositions, we'll know release. If we really know release, we'll know our suppositions. That's when you know the Dhamma that can come to closure.
The above, as translated in "Food for the Heart" p 307 (Ajahn Amaro translation I think) - referenced in the index under "sammuti sacca (conventional reality)"
The things of this world are merely conventions of our own making. Having established them we get lost in them and refuse to let go, clinging to our personal views and opinions. This clinging never ends, it is samsara, flowing endlessly on. It has no completion. Now, if we know conventional reality, we'll know liberation. If we clearly know liberation, we'll know conventional reality. This is to know the Dhamma. Here there is completion.
My suggestion is the way there are using the term, is what the "two truths doctrine" is pointing at. Regardless of whether they are explicitly developing that notion (which they don't appear to be). That "sammuti" is the crucial word here, I think is quite interesting, and I doubt it is simply coincidence.
"When one thing is practiced & pursued, ignorance is abandoned, clear knowing arises, the conceit 'I am' is abandoned, latent tendencies are uprooted, fetters are abandoned. Which one thing? Mindfulness immersed in the body." -AN 1.230