Spoiler
I GUESS,
It's purely a plot counterweight for Dave of Route A vs B+D. Allowing Route A to be become stable/"main-route".
Dave has actually no real Reason to trust Oz in the first place; Oz accused one of Dave's friend being a potential murderer. It's imo more realistic that Dave's trust into his friend would encourage him to reavel Oz on Day 8/9.
On Route B/D, Dave will uncover Oswins body, being stabed. And on Route A we got the Day 11 password, that shows Oswin being alive. So with these two traumatic memories imprinted into the Dave of future interrations, Dave will 99% choose not to reveal Oz.