The FFT does polynomial evaluation at the complex roots of unity. The NTT is the same concept but for the roots of unity of a group of integers, when there are such roots.
Given an implementation of the FFT, can it be used to compute the NTT? I ask because it seems not possible, as the NTT is integer based and the FFT is always complex based thus will have imprecisions, but I've seen someone say they would be able to do it
Your question is confused. Obviously we need to assume that there are no imprecisions in the FFT implementation, and that the input signal is integer valued, so we are given $X_k=\sum_{n=0}^{N-1} e^{2i\pi nk/N} x_n$ in the form $X_k=\sum_{m=0}^{\phi(N)-1} c_{k,m} e^{2i\pi m/N}$ with $c_{k,m}$ integers. Pick a $N$-th root of unity $\zeta_N$ in some ring $R$, then $Y_k=\sum_{m=0}^{\phi(N)-1} c_{k,m} \zeta_N^m$ is the NTT of $x_n$ in $R$.
In this sense yes you can obtain the NTT from the FFT.