Chazal aren’t telling stories, they are teaching Torah. Often you’ll find different depictions from different places in Chazal. In the Medrash you can see more to the conversation that Reb Yochanan Ben Zakay had with Vespasian, than what the Gemara mentions. It is not a contradiction of the facts, it is merely a difference of depiction. Each one is pointing out the important facts.
If we would read about our time in Chazal, we would also be surprised at what is left out. As the Maharal often explains, what we see in the Gemara is Chazal’s perspective of what is important and noteworthy.
It may be that Avaraham Avinu said those words exactly, and it can also be that he didn’t even mention those words at all. Chazal are telling us what his answer was, in essence.
To further explain this concept, if I were to tell you that a fence tells you not to enter, even if it is very simple to step over it, you wouldn’t ask, ‘but a fence can’t talk!’ Actually, a fence can talk, albeit it can only say one thing. It also does not have a choice to say it or not. Often, something is considered said, when actions are what spoke it.
Nobody listened in to the conversation of Avraham and Eliezer. Chazal knew what the reason is that he didn’t want to be Meshaddech with him. Chazal also Darshened from the Pesukim that Eliezer hinted that he would want to be Meshaddech. The answer is implicit in Avraham Avinu’s actions. Eliezer might have understood himself or he might have not. If the latter was the case, then Avraham Avinu answered him, surely in a nice way.
By the way, it says that after this Shlichus, Eliezer’s status was changed to Baruch. So it definitely wasn’t a personal insult. It was a Yichus issue. We find in the Gemara an instance where a Talmud did not want to marry his Rebbe’s daughter because he felt that his Yichus is better.