Do the QCD sum rules support four-quark states?

We test the validity of the QCD sum rules applied to the light scalar mesons, the charmed mesons D-s0(2317) and D-s1(2460), and the X(3872) axial meson, considered as tetraquark states. We find that, with the studied currents, it is possible to find an acceptable Borel window only for the X(3872) meson. In such a Borel window we have simultaneously a good operator product expansion convergence and a pole contribution which is bigger than the continuum contribution. These results may indicate that light many-quark states cannot be considered as resonances separated from the continuum.