Available data on the $X(3872)$ lineshape have been fitted with a Flatt`e parametrization derived from an effective Lagrangian in which $X$, $D$, and $D^{*}$ are all elementary fields. A molecular $X$, i.e., a deuteron-like bound state of $D$ and ${\bar{D}}^{*}$, must instead be described by an effective theory where the $X$ field is initially absent or introduced as an auxiliary, unphysical, field, yielding a lineshape parametrization that differs significantly from the Flatt`e one. We demonstrate, in the analogous theory of nucleons with an auxiliary deuteron field, that this parametrization gives a fully consistent description of $np\to \mathrm{\text{deuteron}}\to np$ scattering data, and motivate applying the same method to the $X$ lineshape. \textcolor{red}{The analysis proposed here is novel and has not previously been carried out on the available data.