What you can do is call this page through a microflow. You can first create an object of AssetTransfer (GiftImage), Then create an object of AssetDetails(Gift).
While creating AssetDetails assign AssetTransfer object to it
This should make your your comments editable.
If you are already having an AssetDetails object, just pass that as parameter to microflow and create AssetDetails object and add to AssetDetails object
First thing to check would be access rights, but you have already checked it.
Check the editability of AssetTransfer data view, it might be set to No.
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It is possible that the AssetTransfer object is not created and not associated with Asset. Can you check this?
I tried to do the same earlier but the mistake was that I had the existing assetdetails object and I was creating AssetDetails again in the microflow which was causing problem. Below is the modified microflow that worked. Thanks for the help :)