Steph was definitely being portrayed as a more serious, if still enthusiastic, vigilante. And they'd had Batman express some approval for that by having him reveal Tim's identity to her; I forget the exact circumstances, so it might have been less clean cut then that, but he clearly trusted her with sensitive information. Plus, the idea of Batman firing her for "not following orders" fall flat when you consider how reckless and impulsive Tim's actions had been in putting on Jason's outfit in the first place. And everyone at the time seemed to be a bit confused at how the events fo her firing went down; the concensus seemed to be it was a manufactured break-up that made little sense. It was probably the result of editorial giving the writers the twin instructions of trying to squeeze some fan support out of the short tenure they wanted Steph to have as Robin, and yet still have her screw up so that it was her fault that she lost the suit.
If I can add another issue that people found hurt War Games when it came out, the way it interacted with Devin Grayson's Born Again retread in Nightwing really didn't help either story. The people who hated the stuff going on in Nightwing, like the rape of Dick Grayson and Tarantula and the dark tone of the story, approached the War Games crossover with the same bitterness, and the bad rep kind of spread out that way, making people who didn't read Nightwing irritated at the same stuff. And to those few (or quieter majority, whichever) who found the story engaging, War Games interrupted the story and killed a lot of momentum and clouded important elements; an example would be Tarantula getting a story where she was ostensibly allied with the Batfamily, when she always seemed to be more of a combination of Typhoid Mary and Elektra at their worst.