I did this with my first home purchase (although not intentionally to get a better deal, I just didn't see the value in engaging a realtor). Saw a home on Zillow, emailed the agent, scheduled my own showing, and put in an offer without a realtor.

Needless to say, I probably got some preferential treatment since, if the transaction closed, the seller's realtor gets double the commission.

It's called "dual agency" and I think it's illegal in some states (for good reasons). When realtors are acting as a dual agent, representing both buyer and seller, there are strict rules they're supposed to follow to prevent a conflict of interest, but in practice it's difficult to make sure everyone is playing fair. I'm pretty sure the seller needs to sign a consent form with their realtor in order for them to represent both sides of the transaction.