Firstly petty downvoting doesn't make you correct and I can do it right back to you
You're confusing the timelines.
Uh No I'm not
When he said all those things later, he was calm and collected.
You know why we don't allow lie detectors as admissible evidence right? Same principle here
Other than the fact that he promised them (and had the ability to do so)
No he actually didn't he just assumed that Ros would give the all clear once he was proven right, He was also shamed infront of every character as being not really anyone with any real power so they have no reason to believe he could make such a promise.
Nobody helped him for free.
Only because the plot bent over backwards to accommodate him, He was a nobody with no real standing making promises they had no way of knowing if he could keep or not
The final arc was pretty poorly done and has some huge logic leaps, It mostly makes sense for the audience because we see the deaths and mistakes. Everyone thinks he is batshit crazy