Doesn't the browser's internal resolver use an external recursive server (either the host's configured ones or browser-determined ones)? Chrome does, AFAICT. As opposed to being a recursive resolver itself, it just implements a caching stub resolver.
The remote DNS host for sketchy-service.com doesn't see your IP address, they see the recursive server's address.
network.dns.disablePrefetch True
network.prefetch-next False