From the paper: "Our threat model includes attackers controlling network routers near the legitimate DNS servers. It also includes attackers using NSA’s QUANTU

From the paper: "Our threat model includes attackers controlling network routers near the legitimate DNS servers. It also includes attackers using NSA’s QUANTUMINSERT man-on-the-side attack technique (no relation to quantum computing), which injects fake responses to DNS queries before the real responses arrive (see, e.g., [32]); the real responses are then ignored." Their proposed ways to tackle these (following the above, see the paper) seem decidedly imperfect though.