In "Samaritan Snare", Picard was framing the story as a cautionary tale. To that end, he removed or elided parts of the story that might make Wesley more sympathetic to his past self, the self he doesn't want emulated.
WESLEY: Really? Then what happened?
PICARD: Nothing. I was no hero, Wesley. I was an undisciplined, loud-mouthed, opinionated young man who was way out of his league. I learned a very hard, very painful lesson that day, but I learned it well. I hope you never have to learn it the same way.
In "Tapestry", he clearly still regrets that the incident ever happened:
PICARD: I was a different person in those days. Arrogant, undisciplined, with far too much ego and too little wisdom. I was more like you.
Q: Then you must have been far more interesting. Pity you had to change.
PICARD: The pity is that I had to be impaled through the back before I learned that lesson. I started that fight with those Nausicaans. I started it because, because I was young and cocky. If I'd been more responsible in those days...
The details of the fight itself in Tapestry are pretty faithful to the description in Samaritan Snare, down to the stress-induced laugh he gives at the moment that he's stabbed. So I would conclude that it's not a matter of ignorance of the original script, but rather a deliberate modification. Assuming that we're not meant to conclude Picard's memory is faulty, it seems like the most straightforward reason for him to frame the story the way he did is to make sure it leaves the correct impression on Wesley. As with keeping his heart issue a secret in the first place, it's a matter of "image".
More speculatively, it's possible Picard is misremembering events in "Samaritan Snare". It was more than 40 years ago, after all. Picard's memories might be influenced by his guilt and regret, focusing on more negative aspects of the encounter and leaving him to fill in the rest. Or, more innocently, he could be conflating it with another incident where he encountered Nausicaans, such as the time in his sophomore year he begins telling Riker about in the denouement of "Tapestry".