I admit that data is hard to find, but that's not a reason to discount rational exploration of this issue. There's plenty of anecdotal cases for it, just see the devastation of Detroit, for example.

As to your claim, throwaway as it may have been, here is why I think it to be wrong.

First of all, police, firefighters and other public services rarely use highways in urban areas. The reason for that is that urban highways are few in number due to their monumental construction costs, so each highway tends to be a few miles away from the nearest parallel highway. As a result, going from A to B in the same city is often faster on arterials than on highways for trips that are 6 miles or less, because the detour to access the highway is longer than the time gain from using it.

Second, highways do speed up longer distance travel, but how much of a benefit is it really? That depends on the kind of travel. As I wrote in the article, rural highways that connect regions together serve an important economic role by helping to speed up the transport of goods and people between them. However, commuting is quite a different beast, because with regards to commuting, there is a phenomenon called "Marchetti's constant", people tend to make choices of location for their residence and their workplace to maintain a commute time of roughly 30 minutes on average, because people understand distance as travel time, not as actual distance. So when you speed up travel inside a metropolitan area (from suburb to city/other suburb), what you do is that you incite people to live further and further away from their workplace and from the stores they patronize.

Therefore, urban highways do not really lead to a reduction of commute times overall (some may have that benefit, but rarely is it generalized) but rather to an increase in distance driven. Which leads to more pollution (though often less concentrated), higher transport costs and a development pattern that makes transit non-viable, therefore forcing people to buy cars to access jobs and services.

An example of this is that in 1972, a study of commuting time and distance revealed that the average commuting time for people commuting 20-24 miles to work was 36 minutes, just 6 minutes more than for people commuting 11-14 miles. In other words, an increase of commute distance of 100% was associated by an increase in commute time of just 20%.
http://www.nber.org/chapters/c8824.pdf (table 6.7, page 19 of pdf)

So higher speed was correlated with longer commute distances AND with longer commute times. Correlation is not causation, but that should give people pause when they claim to want faster roads to reduce commute times.

So higher mode share for cars and greater distance traveled means more pollution, more wealth expanded just to provide transport (which consumption, like electricity, has no good in and of itself). That's a drain on the economy.

Now, because I'm nice, I'll give you one thing: highways allow cities farther away to become economically integrated, resulting in much bigger metro areas. Since much of the modern economy gains from concentrating people and resources in an economically integrated area, this may be seen as a positive. However, what we've seen in Asia and Europe is that in the absence of highways, metro areas can still be just as populous, concentrating as many people and resources in one economically-integrated region... that region just happens to be much more compact, often concentrated around train stations, with highways going around inhabited areas, connecting industrial areas, serving essentially for trips to and from other regions.