An image can be resized by changing the DPI. The more pixels per inch a photo has, the smaller it will be displayed. This allows the image resolution (and, thus, quality) to remain unchanged. However, file size will remain unchanged.
I'm certain this is not the type of "image resize" the product is doing... i.e. changing the DPI. I'm sure they're talking about resizing such as taking a large 4288x2848 JPG that might come out of a DSLR or phone and resizing it down to 1280x1024 or something, in order to send it out on an email or whatever.
Now JPG is already a "lossy" compression of the underlying "raw" (uncompressed) image to begin with, even at high resolution 4288x2848. You're already losing image information with the video-compression technique called JPG, although it will still look "superb" at 4288x2848.
If you use an image editor like Photoshop, when you "adjust image size" you can play with BOTH the DPI as well as the image dimensions (in pixels). You can change one or the other or both as part of the "adjust image size" function. As you mention, playing with just DPI reduction will have the instant simultaneous effect of also making the outer dimensions of the image reduce, but the new JPG will again have to go through another "lossy JPG re-compression" from the now re-sized original, and on better image handlers like Photoshop this also has a customizable user-set "quality" value in the compression to represent the compromise between true image quality (when displaying it) and file size.
Again, in my opinion there's just seemingly no way you can't do "harm" to original image quality by re-sizing it.
Image size reduction and compression are two different animals.
Certainly. But when you reduce image size and want to create a new JPG from it, you need to do a new JPG re-compression... which itself is defined as a "lossy" compression method with a "quality" variable to define the user-acceptable compromise between "eventual image display quality" vs. file size.
This is all a "compromise", and is just a way of minimizing image quality reduction if possible. But it is NOT the original, especially when you're starting from an already "lossy compressed" JPG instead of the "uncompressed original" RAW (or NEF, or whatever) format from the camera.
I took a quick look at the web page in the link and didn't see exactly what kind of resizing the program does.
I looked at that web page for the product as well, and also saw nothing mentioned about this subject. I suspect OP probably made a subjective comment, meant to imply "does an EXCELLENT job of resizing" (i.e. resulting in "no or very minimal visible reduction in image quality", at least given the size of the original and re-size and the method and quality of display to a monitor, TV, phone screen, etc.).
Again, I believe we're really talking about "subjective reaction to the re-sized result", rather than technical objectivity.
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