I completely understand what Obama was trying to say, and he IS being taken out of context. But the ridicule isn't necessarily misplaced in the end. What he is saying is not completely correct, and shows a lack of understanding on how our "system" that he refers to actually came (and comes) into existence.
The first issue is the suggestion that government builds the system and then businesses and entrepreneurs come in and use it. That is actually exactly backwards. This line of thinking suggests that America was built like those vacant business centers in China. As if the government anticipates the need for a bridge or a road, so it builds one and then businesses build around it. It doesn't happen this way at all. The reality is that the commercial buildings and the houses of employees are the driver of the "system". Not the result of it.
If I want to build a new structure, I don't go around searching for a new road that the government has built that is surrounded by available land that they are handing out. I go look for a suitable location for my structure. Then I try to convince the private owner of that land to sell to me. If there is already "system" there that I will be hooking into, then I pay a direct fee (impact fees) to extend that portion of the system to my structure. This is also what all of my neighboring businesses did throughout time. Each time a developer wanted to build somewhere that the system didn't reach to, they were responsible for paying for the expansion to their location. Ask a developer why he can go out and buy acreage for $20K/acre and then sell a 1/4 acre parcel for $70K. He was responsible for the cost of extending the "system" to those lots. Once the system has been expanded, the buyer of those lots is purchasing the land plus the system, from the private developer who already paid for the system expansion in the first place.
Each time a piece of real estate is sold, the new owner pays an increased premium for the expanded system around them. A school, church, and strip mall go into your neighborhood; what happens to your property value? The structure itself is actually depreciating in value over time, as it has a limit useful life before it must be replaced. But the system around it keeps getting more valuable as it expands. So subsequent buyers keep paying more and eventually the value of the system will exceed to value of the structure, to the point where the structure will be torn down and replaced by one that can better take advantage of the expanded system. But all along the way, each new owner pays an increased premium for the system he uses.
If there are no roads to such a location, a couple different things might happen. If it is a private business complex that will not contain through streets, then the developer is completely responsible for the cost. If the developer simply creates through streets that would connect other portions of the road network, then he only pays a portion (frequently 1/2) and the local tax payers come in and foot the rest of the bill because they will be benefiting from a more complete network.
So at this point, not only have the private developers paid for the direct cost of expanding the system to their single location, but also are continually paying for expansion to other areas, as well as higher premiums for the system each time they expand their business.
In the end, the government plays a single roll. They are the planning organization that attempts to zone things out based on intended use. Each incorporated city area has agreed at some point that residential should be located by residential and commercial by commercial. We've appointed city councils to regulate this. We didn't appoint them to build it. Just to make sure that developers don't run amok and create an inefficient network.