Umm....no. If you do not have a buyer's agent, the selling agent will keep the whole commission.
There is no reason not to have a (good) buying agent, there is a lot more with buying a house than just agreeing on the price.
I already addressed the second half of your post. Here's my view on the first half of your post.
If you have real-life experience, feel free to contradict the following.
Scenario:
House lists for $100,000. Commission is 6% (in my area, typically half for Seller's agent, half for Buyer's agent). Seller demands that he at least gets $94,000.
Buyer 1:
Buyer has a buyer's agent.
Buyer offers $100,000 to get house. Seller gets $94,000, Buyer's Agent gets $3,000 and Seller's Agent gets $3,000.
Buyer 2:
Buyer does not have an agent.
Buyer offers $97,000.
Seller's Agent can choose to lower his fee to a flat $3000 and the Seller still gets $94,000. Or he can hold out for the full 6% and not make the sale. In a lean market, I think most Agents would just take the $3000 and call it a good day.
Rationally, for both the Seller and the Seller's Agent, Buyer 1 and Buyer 2 are exactly the same. This, of course, does not take into account any externalities.
As I stated previously, I have seen some people write on the internet that they believe they saved money by not using a buyer's agent. Whether or not this is true, I don't know.
I have also seen others (mostly real estate agents) claim that buyer's agents actually save their clients money, by pointing out things wrong with potential homes, or pointing out certain things that affect a home's future price (e.g. three years worth of construction work across the street will start next month or a new school is being built a few blocks away).