I have a 300dpi image on a layer with a transparent background.
1. I select the image using the selection tool
3. New document by using the exact image size
4. Pasting the image on a new layer
5. Scaling the image down using 72dpi
=> The scaled image has a 1px lighter
border around the image
I need to scale the image up again in order to eliminate the 1px border.
It's annoying. I don't want the image to obtain a slightly lighter 1px border around the image after the scaling down process.
That does not happen on my machine with any version of Photoshop I have installed, I have CS2, CS6, CC, CC 2014, CC 2015, CC 2015.5 and CC 2017 installed. Try using menu File>Place and use the place transform to size your image for the document you working on. Also make sure you zoom to 100% when you judge. Viewing at any other zoom percent you are not looking your documents pixels. You may or may not see some scaling artifacts like layer edges. Photoshop scaling is done quickly for performance at some zoom percent Photoshop scaling looks very bad. You not looking at your actual documents pixels.
Changing a document resolution to 72DPI does not change a single pixel. You need to resample the image to change the number of pixels and when you do that you wind up with a new resized image the original image is out on your disk and in Photoshop history.