Yes, and it could be the hosting.
Is it hosted on professional servers?
What does a simple test such as ping, or traceroute indicate?

Hi engine,

Yes it's hosted professionally, there are other websites on the server that don't experience the same issue, which is one of the reasons we're so confused.
The ping results show an average of 8.51ms response time.
It's almost like the data that Google's got for Page Speed Insights is coming from users with really poor internet connection...

Thanks,
Matt

Matt, what about the possibility that you're seeing cached data (which will seem much better, and that the problem is with the site?
Also, consider that testing from a different location will show different results: For example, if hosted in the U.S, and tested from Europe, it may show different results if hosted in U.S. and tested in U.S. Thant's one of the reasons why I suggested a Traceroute test.

With any site test you should consider that the site might just be a bit slow. For example, a database driven site might be slower or faster than a smaller static site. Or it could be graphics that need optimising, etc.

There are other test tools out there to try.

Another test to try, if practical, is to try hosting the site temporarily elsewhere. That's not always practical (site size and complexity), and a last resort, imho.

This smells like testing from another region. Keep in mind that if you test from your country you will have better results, but google may test from where your hosting provider is, which may as well be another country , resulting in worse outcome.

Use ChromeUX reports if you don't already. You'll get a lot more real world valuable data from actual users.

Setup a LookerStudio report and get digging