The Halpern-Läuchli theorem was first introduced for its use in Halpern and Lévy's proof of BPI in the Cohen model. Since then, several other theorems establish emergent connections between variants of the Halpern-Läuchli Theorem and BPI in certain symmetric extensions. In this talk, we develop the forcing perspective given by Harrington's proof of the Halpern-Läuchli Theorem. By doing so, we will more clearly identify a connection between variants of the Halpern-Läuchli Theorem and the existence of certain filters in symmetric extensions. Using tools from the study of BPI in symmetric extensions, we use this connection to give simple positive and negative proofs of new variants of the Halpern-Läuchli Theorem.