Photoshop - images under 300dpi resampled - help please

There's a lot of misunderstanding around the 300 number. It's not sacred.

It's usually treated as a minimum requirement, but it's not. It's a theoretical upper limit, above which any increase is totally masked by the line screen frequency (lpi).

Furthermore, it's not even a sharpness parameter. It's a smoothness parameter. It's the point where it's no longer possible to discern individual pixels. The sharpness, OTOH, the acuity, is determined by the line screen - so maximum sharpness is already achieved at 150 ppi, not 300 ppi.

"This I believe means photoshop will insert artificial pixels and makes a best guess on the colour of these pixels based on surrounding existing original pixels."

Good guess, Photoshop will introduce new pixels based on surrounding pixels, depending on the algorithm in use.

"They are experiencing some trouble with images, and I have provided my explanation above regarding why they should not use resampled images."

Resampling small images, like 300x200 pixels, will most likely result in a pixelated image, depending on the image content. That image is likely scaled down and saved, in most cases, for the web with low-quality settings for faster loading on the website. Resampling even larger images will often appear unacceptable as well. Resampling a 5000x3333px TIFF image derived from the original RAW file may not look bad; in fact, it should look acceptable, depending on many factors—do not misunderstand that any image will look good. Primarily, it depends on the image itself, its sharpness, the quality of details, and scaling factor. It really depends on what you have to start with; sometimes it's not acceptable, while other times it can be fine. Resampling down or up will always result in a loss of quality. Scaling down is almost always acceptable unless there are small details that must be visible, while upscaling can be more problematic. Sometimes it is acceptable, while other times it is not, which depends on many factors.

My view: Where possible all images used in a design for print should be 300dpi (true resolution).  Images that are say 150dpi can technicially be made 300dpi by resampling the image in photoshop.

By @Lawtz01

When viewed at arm's length, the final physical reproduction size for halftone printing should ideally have an image resolution (PPI) of x1.5-2 times the halftone line screen (LPI) value. So, a 150 LPI halftone would require 225-300 PPI image resolution at 100% print size. This also depends on image content.

The first thing to do is use Image > Image Size with resampling turned OFF to resize the image to the final desired 100% printed scale to see what the effective resolution of the image is. The effective resolution is the "true" resolution of the image when sized for print. This could be lower than the ideal target of 300, or it could be higher. Once you know the effective resolution, you can decide to leave it as is, downsample or upsample.

There are many ways to upsample, it depends on the resampling algorithm and the image content on the results.