Em, this may not be of much use but I'd have thought that the native PPI of an image is directly related to how large you print your photos. The images are 16MP whatever way you look at it, but the native PPI for a 8"x6" print will be greater than the PPI for a 12"x9" print.
The ppi recorded in the image means exactly nothing - it's the number of pixels that matters (16MP for the GH4). If the camera recorded the image with, say, 360ppi then (assuming it's still 16MP) the only difference would be that the number 180 was replaced with the number 360 - the images would be identical. As Levster said, the only time the ppi means something is when you print the image (or view it at a particular size), and then it's determined by the print size and number of pixels, not that value recorded in the image.
Unfortunately the JPEG standard insists that something is recorded as the ppi, even when it is meaningless...
Just open the image in your usual image editing software, then go to image size and look at how big the image is with that PPI setting, then change the PPI to 360 and see how the image size changes, or change the image dimensions to match you print size and see how much the PPI setting shoots up
If I do this with one of my G6 images which are also 16mb images the same as the GH4 the images are 4608x3456 pixes and at 180ppi they will print to 25x19 inches but at 360ppi they will print at 12.8x9.6 inches.