That's not true at all. I have seen northern lights with my own eyes that were more neon green and bright purple than any mainstream photo.
But what sort of eyes are those?
Priming the opsins in your retina is a continuous process, and primed opsins are depleted rapidly by light. Fully adapting your eye to darkness takes a great deal of darkness and a great deal of time - on the order of an hour should set you up.
Most human beings in arctic regions live in places and engage in lifestyles where it's impossible to even come close to attaining the full light sensitivity of the human retina in perfect darkness. The sky never gets dark enough in a city or even a small town to get the full experience, and if you saw your smart watch five minutes ago you still haven't fully recovered your night vision. Even a sliver of moon makes remote dark-sky-sites dramatically brighter.
Everybody is going to have different degrees of the experience because they'll have eyes with different degrees of dark adaptation. And their brains are going to shift around the ~10^3x dynamic range of the eye up or down the light intensity scale by a factor ~10^6, without making it obvious to them.
(Edit: it was still super-cool even if grey-ish, and there was absolutely beautiful colors in there if you could find your way out of the direct city lights)
I've also seen the northern lights with my own eyes. Way up in the arctic circle in Sweden. Their color changes along with activity. Grey looking sometimes? Sure. But also colors that are so vivid that it feels like it envelopes your body.
Then again, the average viewer in Seattle this past weekend is hardly representative of what the northern lights look like.
The H in HN stands for Hubris.
Phone cameras have a Bayer filter which means they only have RGB color-sensing. The Bayer filter cuts out some incoming light and dims the received image, compared with what a monochrome camera would see. But that's how you get color photos.
To compensate for a lack of light, the phone boosts the gain and exposure time until it gets enough signal to make an image. When it eventually does get an image, it's getting a color image. This comes at the cost of some noise and motion-blur, but it's that or no image at all.
If phone cameras had a mix of RGB and monochrome sensors like the human eye does, low-light aurora photos might end up closer to matching our own perception.