There are quite a few examples in additive combinatorics of theorems or tricks that were talked about and 'known' a few years before anyone published a proof of them.
For example, let $\phi(n)$ be the largest number such that every set $A$ of $n$ reals contains a subset $B$ of cardinality $\phi(n)$ such that no element of $A$ can be represented as the sum of two distinct elements of $B$ (‘$B$ is sum-free with respect to $A$’).
It was remarked by both Klarner and Erdős that $\phi(n)\geq\log n-O(1)$ for large $n$, but it was ten years before Choi published a proof of this (a simple application of Turán's theorem on independent sets in graphs).
Presumably phenomena like this occur because those who think of it see it as too simple or straightforward to be worth the bother of publishing.
A different type of example is the idea that if $f:G\to\mathbb{C}$ is a function on a finite abelian group $G$ with a small $L^2$ norm, then it can be decomposed as the sum of structured parts (with a small error term).
For example, $f=f_1+f_2+f_3$, where $f_1$ is the linear combination of a small number of characters, $f_2$ is Gowers uniform and $f_3$ has $L^2$ norm less than $\epsilon$.
This kind of folk theorem arises because it is a commonly applied heuristic that can be made precise in a variety of different ways, often jury-rigged for a specific application.