Huh, how do you imagine that would work? This "scan" is happening inside client-side javascript, delivering the file through a proxy wouldn't "detect" anything about the proxy.

I imagine it may not be a proxy in the true sense, but a headless browser that's "proxying" the application process rather than the network traffic itself.

Proxy is being used in the traditional sense here. It’s common for a business (scam or legit) to handle visa applications on behalf of customers.