This error only comes up if you try to import files into Premiere Clip which are not in your Camera Roll.
You can only import the files which are in your Camera Roll.
If I am correct, iCloud Photo Library is causing this. On my iPhone 6 (iOS 9.3.3) I have enabled "Optimise iPhone Storage" which automatically deletes photos that are uploaded in iCloud. This is very good feature for saving space but it's causing problems with basically every photo/video app that doesn't use stock media picker that is provided in iOS (UIImagePickerController). I've tried a few ways to download the picture I wanted to add into Premiere Clip, I copied it, I duplicated it, I tried to send it via iMessage - every process shows either "Processing..." or "Downloading..." but still no success in Premiere Clip, but you can try it out, maybe Apple fixed it in iOS 10. Other than that I assume the only way to fix this is to set iCloud Photo Library to "Download and Keep Originals", unfortunately I can't try this out for you because I don't have enough space on my iPhone.
I’m having this same issue. My images are in my camera roll but I think I see the issue: with newly shot/imported images — ones that are still in the process of completing their uploa/sync with iCloud, they appear to be unavailable to Adobe Clip/Premiere. You’d think Adobe would fix this as it makes using the mobile app very limited.