Lucy, you're right that they load images 'cold' but they still manage to take a copy(will need to dig deeper to find out how). I've had hotlink protection on for ages, exactly as in the opening post, and Google indexes all images anyway. They display their own cache copy in image search results, never my original images hotlinked.
I've checked in both new and old browsers, I don't see any difference. Google links directly to my page from two places(the image is linked as is the visit page button) and to the image url once(view original image). With the hotlink protection mentioned here the 'view original image' fails(403 due to no referrer) but the links to the page the image is on do not.
As long as Google indexes the images using their own cache copy but still links the images to my pages then I have no plans to stop using hotlink protection.
Lets take a step back
Many webmasters were hit with a 60-70% image traffic loss when the new Google image layout was rolled out, it was discussed here and written about on searchengineland as well. An excellent writeup with with graphs was written here: [pixabay.com...] The reason for the loss was said to be because full sized full resolution images were on Google in a way that doesn't encourage visitors to actually leave Google image search. Your images used to be displayed on a new page with your website loaded in the background but now the images are loaded right into the image search results page without your site in the background. It's infinitely easier to switch to other images now with no benefit to webmasters, many images even have competing image thumbnails from other sites shown beside them.
Google countered the claims of traffic loss by stating that most webmasters were getting a 25% increase in image traffic due to now having two links lead to your pages instead of just one. The obvious discrepancy aside the fact remains that it's easier to stay on Google image search to see full sized full resolution images than it is to visit your site. Also, without your page being shown in the background there is nothing enticing the visitor to see where the image came from.
- Watermark overlay images when loaded on Google image search with text such as 'click for full resolution'. This immediately increases your image CTR but traffic from this method drops steadily over the following months. Reason? Only google knows for certain but it's likely that your image metrics suffer and slowly lose rank, too many backpage buttons being pressed.
- Redirect 'view original image' link so that visitors land on the page the image is on and not on the image url. This is an involved process and it sends less image traffic to your site than watermark overlays do but the traffic does not decline in the same manner over time.
- Inline watermarking your images. Add a 20 pixel strip to the bottom of all images and, using css, float a 20 pixel div over this section so that visitors on your site do not see the watermark strip. The text in your watermark strip might read something like 'click to see this image on example.com' or something similar. Google image search will then display the full image with watermark strip but it doesn't impact your visitors at all, they never see it on your site. No official word on if this is considered showing visitors something different than you show search bots but it is effective and does get indexed.
- robots.txt block google's image bot? Surely giving yourself a 100% image traffic loss can't be the best solution.
In all of the above you can safely leave hotlink protection on, exactly as shown in the opening post, and it will not interfere with any of the current solutions. Why not? Image hotlink protection is a hurdle Google has decided to jump in order to stock their image search results. Since that's how they deal with image hotlink protection you can have it on and not lose search traffic.
My answer to the original question is that yes, it's safe to use hotlink image protection as it is a common practice in protecting images. Google ignores it and shows a copy of the image anyway.