Even if "that" refers to infrastructure, he would be dead wrong.
First of all, infrastructure is not built for a particular business or businesses. It's was built --with a HUGE emphasis on "was"-- because it was identified as a necessity for progress and other factors. Most roads in the US were built decades ago. The project started in 1956. It's interesting to read the "Financing" section on Wikipedia:
http://en.wikipedia.org/wiki/Interstate_Highway_System
This and the railroads were not built for any particular business but rather for reasons spanning from national defense to, yes, economic growth. The system was paid for and is being paid for by everyone in some form or another and everyone benefits from this.
Obama's statement, to paraphrase, went something like: "If you have a business...and are successful...you didn't build that". Some argue, probably correctly, that he was referring to infrastructure rather than the business itself.
In isolation that might be the case. But there was more. He also said a few things to the tune of, again, paraphrasing: "if you are successful...it isn't because you work hard or you are smart...lots of people are smart and work hard". And, right after that, he wen't into the "you didn't build that" paragraph. The implication is that your success is due to, in large part, to government.
I would argue that unscripted comments like this one tend to reveal how someone thinks. And the not-surprising revelation in this case is that Obama has deep socialists beliefs. How else would you even consider the idea of equating the success of any business TODAY with the construction of infrastructure DECADES AGO? You have to construct a certain model of reality before you'd even utter such words. Someone like myself, an entrepreneur through and through, would never, ever, even consider saying something like that. Government has never been the source of my success or failure.
His statement is like arguing that a fellow launching a web development business today owes his success to government because the desk he bought was shipped via railroad and the highway system. That statement would be deemed ridiculous to a ten year old, much less intelligent adults.
Yes, infrastructure benefits everyone. Millions of people use (and pay for it) every day to conduct their lives. Not one person owes their success to infrastructure alone. Once in place it is deemed a given. Infrastructure was a natural side effect of the exploration and expansion that took place in this continent. Today, there's far more that goes into becoming successful in life privately and in business than the pre-existing infrastructure.
There's a reverse side to this argument. If government is the source of my and your success because it built infrastructure (that we paid for). Then, they ought to also be responsible for my and your failures. You can't have it both ways. The infrastructure in Los Angeles, as an example, is in a dire state of disrepair. Just drive on the 405 or 5 Freeways --to name a couple-- and you'll know what I mean. I have not seen government make a concerted effort to really maintain and repair these roads in probably twenty years. I used to drive sports cars with stiff suspensions. Your bones would rattle when going over these roads. In sharp contrast to this, the last time I was in Munich, the Autobahn felt as smooth as a billiards table.
So, if government is responsible for your an my success then it is also responsible for your and my failures. I don't mean this seriously. It's a ridiculous argument, of course. Just as dumb and ridiculous as Obama's claim that businesses owe their success to "the collective".
If you built a country, and were successful, you didn't build that! It was the Spanish with their ships and all of their national infrastructure that enabled you to be able to have a successful country and, yes, enabled that guy today to open a taco stand and experience success. Ridiculous.