Quod Verum Meum Est

A few weeks go I sent the following message to Riverside High school, by e-mail:

In my day (1974-77), Riverside High School’s motto, quod verum meum est—“What [is] true is mine”—, was officially translated as, “That which is true is mine”.  The motto was adapted from the younger Seneca’s defence of literary appropriation, quod verum est meum est (Epistulae I. xii, 11)—“what is true is mine”.
Now, however, I see that you translate the motto loosely as, “All that is true is mine”.  Where is the Latin word for “all” in the motto?  L. Annaeus Seneca was a fairly bright bloke, who was a recognised master of Latin; had he wanted to say “all” rather than “what” he would surely have used a suitable Latin word for “all”.
Latin had several words meaning all: cunctus, omnis, and totus; but none is in the motto.
Could it be that in recent times someone decided that “That which is true is mine” sounded clunky, or did some bright spark decide that if what is a true thing be mine then, logically, all that is true must be mine?
It’s quite a step from claiming that what is a true statement may be appropriated by me to asserting that all true things belong to me.  If any of the buildings of Riverside High be true, by the way, I hereby claim ownership; feel free to send me a few reams of cartridge paper, the odd laser-printer, a selection of brass instruments, and a cash-box or two: they’re mine.
I advocate the more accurate translation, “What is true is mine.”

I have so far received no response.