Using '|' from Bash's if construct prevents variable being set

I've read that you can redirect I/O into and out of various constructs in Bash (such as "if" and "while"). When I was trying this out, I noticed that using a "|" at the end of an if construct prevented any variables that I overwrote inside the if construct from taking effect; but if I use ">" instead, then the variable modifications take effect.

#!/bin/bash

VAR_0='Unmodified'

if true
then
    VAR_0='Changed'
fi | cat

echo "VAR_0: $VAR_0"

###########

VAR_1='Unmodified'

if true
then
    VAR_1='Changed'
fi > tmpFile
rm tmpFile

echo "VAR_1: $VAR_1"

Running Bash version 4.3.11 on 64-bit Linux produces the following output:

VAR_0: Unmodified
VAR_1: Changed

Note the only difference is how I'm redirecting stdout from the if construct. Why is the "|" preventing VAR_0 from being changed?