Of course she could have.
We all could do a world of better things, if we could go back in time.
Buffy made an error in judgment. She knew that then. She felt a tremendous amount of guilt for what happened to Jenny. And, hey, it goes back even further than that. Buffy made an error in judgment in sleeping with Angel in the first place.
The Jenny line, IMO, would have been an incredibly low blow. We all know that Buffy's decision to have sex with Angel was a bad decision...but Giles, at the time, wasn't blaming her for that. He said as much in "Innocence." So for him to change his tune in "Empty Places would have been incredibly unfair..especially since, who could BLAME Buffy for not being able to kill the man who, mere episodes earlier, had been her boyfriend?
The remark fits. Buffy has been known to make errors in judgment. She's human, after all. The only difference is, her errors come with more devastating effects than the average person's. So although the Jenny remark makes sense, I still think it would have been extremely unfair for Giles to bring up right then.
Have a re-read of what you wrote.
You say that it was wrong of Giles to use this BUT Giles then argue that Buffy has made errors in judgement and thats fine, as long as we don't mention them.
The whole scene is the group questioning if this is a good idea based on Buffy's judgement.
Giles doesn't just say Jenny.
He starts because Buffy calls him on what he tried to do with Spike and what he did to Ben.
Spike, at the time, was a Vampire that at anytime could have been called upon by the First to kill everyone in the house.
Buffy was totally blinkered by her affection for Spike. I actually agree with what Giles tried to do, just not his method.
With Ben, Buffy SHOULD have killed him because Glory was still a threat, even if she was a diminished one.
But again, Buffy didn't so he had to do it to protect her.
Giles counter is perfectly right, even if his intention is incorrect.
She does act rashly, she does act alone, even when time and again she has shown that when she works with people the outcome is so much better - because the world is saved!
The problem with saying that Jenny was a low blow and then using 'well after it Giles said it was fine and not her problem' is that this was at the beginning of her relationship.
Over the years, Giles has seen that Buffy makes the same mistake, plays with other peoples lives in this manner.