That's not necessarily true and I can prove it.

Here is a counterexample. Quote:

"GDOT officials are considering raising the speed limit to 70 in urban areas - or places with populations of 50,000 or more. The agency raised the speed limit to 65 mph along a 27-mile stretch of I-285 in November. **Department records show that drivers traveled at 65.4 mph after the limit was raised, compared with 65.5 mph from before.** The limit had been 55 mph."

My preliminary research suggests that raising speed limits on interstates, particularly rural interstates,

can be a reasonable course of action (PDF). But raising speed limits on surface streets is not:

The results of the model estimations showed that, for the speed limit ranges currently used, speed limits did not have a statistically significant effect on the severity of accidents on Interstate highways. However, for some non-Interstate highways, higher speed limits were found to be associated with higher accident severities, suggesting that

future speed limit changes, on non-Interstate highways in particular, need to be carefully assessed on a case-by-case basis.