"Allowed to run" was appropriately imprecise, but not appropriately read into with an inference of lying.
As I said, GHWB wasn't giving permissions, nor did DJT seek one from him, as was appropriate. Jeb's performance was enough of an embarrassment already, or GHWB could have felt or "acted more strongly."
After all, if one looks at the 3/30 1981 (GWHB-Hinckley-Ronaldus Magnus) assassination attempt, a mere 69 days after RWR was inaugurated, one could say GHWB contrastively did not allow RWR to be president, despite its having nothing to do with a permission, per se.
At this late date, we can perhaps reasonably infer that had more to do with GHWB being next-in-line than his enduring animus against conservatives, for surely, his verve against PDJT was relatively greater in that regard, even than against RWR.
In the 2016 case, GHWB allowed DJT to run on the Republican ticket in the sense that GWHB did not forcefully stand in his way.
Nonetheless, we don't have to be mind readers to know GHWB's feelings about the matter:
Of course, PDJT did get in the last licks.