Careful and precise are not the standards for copyright protection. Creative is. In the case of an image which is completely from a single public domain source, there just isn't anything creative being done. You stitch together the tiles in a completely algorithmic manner. If anyone holds the copyright on the resulting work, it would be the person who chose what scene to picture (the user of the software), not the person who wrote the software. That is also the person who put the work in fixed form, another requirement for copyright protection.
I say show me the creativity. I don't see it. I actually don't see much creativity in any satellite photography, but when it comes to creativity from Google in a typical Google Earth shot, I don't see any at all.
The algorithm would be creative, which should be enough. Would you say a painting made using a rubber stamp wasn't creative because anyone can cover stamps in paint and put them on a piece of paper? The creativity comes in making the stamp, and so, what you make with that stamp is copyrightable.