For what I know, nope. He has resigned from any position. I don't know if Mozilla tried to offer him another job or his previous role of CTO, but in a situation like that one he ended in, I think he just decided to sever all the ties.
MoCo's board tried to convince him to stay the course as CEO or CTO, but he felt he should sever all ties with Mozilla to draw fire away from the organization:
The Mozilla FAQ on CEO Resignation says "Brendan was not fired and was not asked by the Board to resign. Brendan voluntarily submitted his resignation. The Board acted in response by inviting him to remain at Mozilla in another C-level position. Brendan declined that offer. The Board respects his decision." [1]
"Another C-level position" definitely means not CEO, and probably means CTO.
So Brendan is not disagreeing with the posting, he's just not stating that he was offered a job as CTO or whatever.
I don't know where cpeterso got the idea they asked him to "stay the course as CEO or CTO", but the FAQ makes it pretty clear he was not asked to stay as CEO, and was probably offered his CTO job back. Are there any other "C-level positions [2]" that he is qualified for? Probably not CDO. ;)
Edit: cpeterso may have been quoting yoric from here: [3] So I don't know where yorik got that idea from. But Brendan corrected his incorrect information, without actually openly revealing what the correct information was.
cpeterso got the idea from other Mozilla employees. The "he as offered to stay as CEO" grew legs when employees started responding on the governance newsgroup to people complaining about the firing. One person (Yoric I think) said he was offered a position. Then it grew to offered to stay as CEO. Then it grew to "Brendan even got angry about being asked to stay on" or some such statement. It's a classic case of incremental additions to an originally incorrect statement.
Brendan set the record straight and after that the official Mozilla line was clarified. The FAQ was updated to be clearer after Brendan made those comments.
I am a Mozilla employee, but I have no first-hand knowledge of what the board did. In Mozilla town hall meetings, multiple board members said they pleaded with Brendan to stay. I don't think they or Brendan would mislead us, so perhaps Brendan is using a very precise meaning of "tried to convince me to stay as CEO."
He does not know otherwise and is mistaken. When Brendan's comment dispelling the rumour that he'd been offered to remain as CEO it was brought up in the Mozilla governance newsgroup and other places. Mitchell Baker clarified that he was not asked to stay on as CEO but was asked to stay on in another, lower level, position. Unfortunately some employees still repeat the false claim.