Please elaborate which statement is false and why.
To describe the uncharged pion in the initial state you will have to project the open $u$ or $d$ quarks onto the mesonic spin zero wavefunction carrying quantum numbers of the $\pi^0$. At the Feynman diagram level, as mentioned in the comments, you obtain the famous triangle diagrams via Yukawa interaction describing the decay, driven by the well known chiral anomaly.
The hadronic mediating diagrams can be viewed as a 'course-graining' or effective description of the underlying quark resolved diagrams. The pion decay rate is independent of the description used under the so called anomaly matching condition, but that is a detail.