WordPress Multi-Site: Get Featured Image from Another Blog

Yesterday, David Bisset posted a tweet asking the following question:

Is there a function similar to get_the_post_thumbnail for multi-site (to grab a featured image from a post of a particular blog id)?

At the time, it seemed that the best way to do so was to use the Sitewide Tags plugin for WordPress, which, I believe, does offer some functionality similar to this (I haven’t used the plugin, yet, so I can’t say for sure).