Mexico's strict gun control hasn't stopped its worst problem: crime

Mexico has very strict gun control laws:

Mexico's gun control laws are much stricter than in the United States. Individuals may purchase pistols or lighter caliber rifles, but only after obtaining a license following an exhaustive background check and then registering the firearm with the federal government. . . .

But voters think that the country's most pressing problem is crime:

People in Mexico have a clear idea of what their country’s most pressing concern is, according to a poll by Ipsos-Bimsa published by El Universal. 21 per cent of respondents think crime is the biggest problem facing the Latin American country. . . .

Gun control advocates claim that the problem is guns from the US. Here is my question: Why is it that if the Mexican's can't control the drug trade, they are going to be able to stop the drug gangs from getting the guns that are necessary to protect their drug businesses?