When a large public procurement takes place, there is no place for emotion. The invitation to tender will contain the rules of the procurement and bidders and the client have to abide by the rules. To get a place on the bidder list, generally, companies go through a pre qualification stage where their track record is taken into account. Once on the bidder list, they will be part of the competition and will stay part of it until is is demonstrated that they have no hope of winning - eg a significant non compliance that the bidder is unable or unwilling to correct, or a gross/substantial change of circumstances of the bidder.
If a bidder is excluded because the bidder thinks the client hasn't evaluated the bid properly or has otherwise failed to follow its own rules then the bidder can seek redress from the courts. Unless there is a gross failure by the client, it is unusual for courts to overturn a client's decision but there might sometimes be a a contribution to the bidder's costs of bidding.
The horror scenario is when the bidder finds that a bidder has found a way to offer the most compliant, most economically advantageous bid, completely within the rules, but is quite different from what the client really wants. Their only option in this scenario is to cancel the procurement and start again. This doesn't often happen.