The perturbative QCD description of high-energy hadroproduction of two hard jets separated by a large rapidity gap void of emission (also called Mueller-Tang jets) is based on a factorization formula of BFKL type that represents exchanges of colour-singlet objects among the external particles. This formula resums to all perturbative orders a certain class of Feynman diagrams that are supposed to dominate the cross-section in the Regge limit. However, the explicit calculations at next-to-leading logarithmic order questions the validity of such factorization when an IR safe jet algorithm is used to reconstruct jets. We show the origin of such violation of factorization, and quantify its impact for LHC phenomenology. In this connection, we estimate the impact of other contributions to the cross-section that are not included in the Mueller-Tang factorization formula -- colour non-singlet exchanges -- that, at low rapidity separation, compete with the singlet ones.