This was never outright stated, but it was heavily, heavily implied by the time the Sarah Connor Chronicles was canceled that there is no reprogramming going on. The Resistance is just not yet ready to believe that Skynet has its own rebels.
2x19, Today Is The Day, Part 2 was, I think, our first direct clue. Here's an extract from the Terminator wikia on the page for Catherine Weaver:
While underway back to the United States, a group of soldiers went to
a storage locker to examine the mysterious box that had been
recovered. Although Queeg claimed to have been instructed by John
Connor to do this, the crew did not trust him and so opened the box.
Discovering a liquid-metal T-1001, Goodnow raised her firearm and was
killed. In the process, the Terminator took her appearance and escaped
by slithering through an air vent.
Before Jesse Flores managed to leave the ship, which they are
abandoning after Queeg is killed for refusing to comply with the
crew's orders, the T-1001 delivers her message to Jesse, telling her
that it is for John Connor. It is simply The answer is "No". Then the
Terminator slithered away through the water. It is presumed that this
T-1001 went back in time, replacing Catherine Weaver to take her place
to create an AI that could be sympathetic to humans, giving them an
advantage against Skynet.
The question posed to the Terminator was asked by future John Connor: "Will you join us?".
The question was repeated again in the series finale. Weaver had Ellison deliver it to Cameron, stressing very, very strongly that had to say exactly those words in that order, and that Cameron would understand what they meant.
And side note, since you didn't follow SCC very closely - I belieeeeve this was revealed to the viewers, but not the main characters, around the middle of Season 2:
Catherine Weaver was a liquid terminator who was building an AI named John Henry - an AI sympathetic to humans that would be capable of going one-on-one with Skynet.