Google can make a change at any time, and without telling anyone they’re doing it. For example, when they acquired Picasa web albums, they shut it down and shunted everyone’s photos to Google Photos. They did this without warning and without redirects. When someone else has control over the links you’re using, you’re at their mercy, and you’re always in danger of a modification on their part that will affect your link. And while Google may link in a similar way for their own logo, they have control over every facet of that process. You don’t.
Another thing to consider is that Google is only providing you an image on another site, not an image on their own site. So let’s say you find an image through google image search on my website. You link to it (as you do in your Eddie Rouse page). A week later, I remove that image on my site. You now have an unruly and broken link, because that google link is no longer going to be valid. So now there’s two levels in which someone else has control over that image that can affect your ability to access it.
But that’s all really the least important parts of my case against linking directly to the google image. More important is code that runs so long that it becomes unruly on your page. That image link is 187 times longer than all of the rest of the text in your HTML file. Not 187 more characters, 187 times the total! I don’t think anyone will look at that and think it’s good code. Especially when there are alternatives (such as through Cloudinary, as I mentioned before) that will provide you with a much smaller character count.