I think you're probably looking at all this a bit too literally. Comic book movies (and movies in general) routinely play fast and loose with reality and have characters saying stuff simply for the benefit of the audience or to get a story point across.
So just because writers have been lazy or sloppy in the past, we aren't entitled to criticize it when it happens again?
And besides, it's not like movie was tracking Jenny's every move. Like many people in the city she was certainly aware of what Zod and his gang was up to, and that they were responsible for leveling much of the city with their machine. And she probably saw Supes and Zod duking it out at some point as well, given how much ground they were covering.
You're forgetting when the line was spoken. When Jenny said "He saved us," Superman had only just arrived in Metropolis. It was before his direct confrontation with Zod had even started. The only thing he'd done at that location so far was to catch Lois after she fell out of a plane and lower her to the ground. That
was when Jenny said "He saved us" -- while Superman was bringing Lois in for a landing, before Zod emerged and their fight started. At the moment Jenny said those words, the only thing Superman had already
done to save anyone other than Lois was destroying the Indian Ocean half of the world engine. And that happened on, quite literally, the exact opposite side of the planet
from where Jenny was, and she didn't exactly have time to get a news update because she'd spent most of the past several minutes trapped under skyscraper debris. So she could not possibly have known about it.
For her to think Supes saved them (or at least had a very big hand in it) seems like a pretty natural conclusion for someone to make, I'd say.
If she'd said it five or ten minutes later, then you'd have a point. But she didn't. She said it at a moment when it made absolutely no sense to say it. Like so much else about this movie, it was tacked on pro forma
without being earned or justified.