Upon further investigation, I think the issue may be related to when the Cache-Control response header is no-cache, no-store in combination with Fastly not respecting those values.
My Fastly CDN was marking what looked like a noscript version of the home page for a web crawler as HIT’s because it must have crawled with the no-cache, no-store value.
Fastly suggests adding an Expires: 0 in situations like this.
I’ve implemented this as suggested by the fastly docs in the meantime.