The gentlemen did approach, and when Mr. Wickham walked into the room, Elizabeth felt that she had neither been seeing him before, nor thinking of him since, with the smallest degree of unreasonable admiration. The officers of the -- -- shire were in general a very creditable, gentlemanlike set, and the best of them were of the present party; but Mr. Wickham was as far beyond them all in person, countenance, air, and walk, as they were superior to the broad-faced, stuffy uncle Philips, breathing port wine, who followed them into the room. (Chapter 16)

Wickham appears to be of a higher caliber than his companion officers who are in general a very creditable, gentlemanlike set. I think one of the reasons Lizzy believes Wickham’s story is that he is a gentleman and she has no reason to think he would lie. I agree the idea of telling Lizzy his story after just meeting her seems odd to me too but is this only a personal reluctance on our part—something we would not do ourselves. Wickham could just be one of those people who desire sympathy from others or he may feel he must explain the greeting between him and Darcy is Chapter 15—he tells Lizzy, “You may well be surprised, Miss Bennet, at such an assertion, after seeing, as you probably might, the very cold manner of our meeting yesterday.” I also agree with you and Kathi, the red flags which suggests to me things are not exactly as Lizzy believes is a few inconsistent comments by Wickham in Chapter 16:

"I have no right to give my opinion," said Wickham, "as to his being agreeable or otherwise. I am not qualified to form one. I have known him too long and too well to be a fair judge. It is impossible for me to be impartial. But I believe your opinion of him would in general astonish -- and perhaps you would not express it quite so strongly anywhere else. Here you are in your own family."

Wickham says he has no right to give his opinion of Darcy because he cannot be impartial but he does actually give his opinion of Darcy’s ability to be agreeable and on much more.

"Oh! no -- it is not for me to be driven away by Mr. Darcy. If he wishes to avoid seeing me, he must go. We are not on friendly terms, and it always gives me pain to meet him, but I have no reason for avoiding him but what I might proclaim to all the world -- a sense of very great ill-usage, and most painful regrets at his being what he is."

Despite claiming himself ready to meet with Darcy he avoids the Netherfield ball.

"Some time or other he will be -- but it shall not be by me. Till I can forget his father, I can never defy or expose him."

He says he will not expose Darcy because of the father but he is exposing Darcy to Lizzy in Chapter 16 and then after the Netherfield party departs for town he exposes Darcy to Aunt Gardiner in Chapter 25 and to everyone I suppose.