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What happens in auctions depends both on the circumstances of the auction and the rules. One possibility is that the bidders have private information relevant to the other bidders - for example some inside information about future conditions in the fuel market. In this case their bid may reveal this information, and this needs to be taken account of in formulating a bidding strategy. However, in the circumstance you describe, it seems a reasonable approximation to think that the bidders profits depend on the cost of providing the fuel, and that they know this cost, while the other bidders do not.

Assuming this case of "independent values," the answer depends on  the rules of the auction. The simplest auction is the sealed bid second price auction in which the low bidder wins, put is paid the second lowest bid. (This basically leads to the same results as the English auction where bidders call out prices until no one is willing to go higher, and the high bidder wins.) In a second price sealed bid auction it is a dominant strategy to bid your own value. This means that knowing the bids of other bidders is no advantage, and the strategy of the 4 competitors will not change. It also means that your firm will derive no advantage from knowing the other bids before placing its own. Indeed, it seems that X should agree to your arrangement, but insist on a second price sealed bid auction, as this is known to yield the same expected revenue as the sealed bid first price auction, and they lose nothing by letting you see the other bids.

However, it seems clear from your question that you have in mind a sealed bid first price auction, the usual type of sealed bid auction. In this setting, you clearly get an advantage from seeing the other bids, and in effect, you bid less aggressively. Your question though is what about the other bidders? X's intuition is "they aren't likely to win anyway, so why bother to bid aggressively." Your intuition is "the only chance of winning is to bid aggressively, so bid aggressively." Unfortunately, I do not know who is correct, nor if this question has been addressed in the auction literature. We will try to provide a more satisfactory answer in a subsequent post.