We prove that the genus-0 sector of the quartic analogue of the Kontsevich model is completely governed by an involution identity which expresses the meromorphic differential $ω_{0,n}$ at a reflected point $ιz$ in terms of all $ω_{0,m}$ with $m\leq n$ at the original point $z$. We prove that the solution of the involution identity obeys blobbed topological recursion, which confirms a previous conjecture about the quartic Kontsevich model.