"General" is not a rank in the Roman world, in the way that it is in modern parlance. At least not until late antiquity, when it becomes a rank in the nobility (duke). "Dux" simply means leader. It is derived from the same root as duco, to lead. Anyone who leads an army is a dux, but a dux is not in and of itself an official position or title. In practice that means that duces are those holders of imperium, magisterial power, who have actual command over an army at any given moment. Originally that would have meant only the consuls, and in the very earliest days before both consuls regularly went out on campaign early in the year (so effectively in almost legendary times, like when Camillus was around) would actually mean only the consul on campaign. By the third century that had expanded to include the praetors as well, and the increasing use of promagistrates in the second and especially the first century meant that eventually warfare was more likely to be conducted by a propraetor or proconsul than a sitting praetor or consul.

This distinction is vital, because it's not that generals--i.e. leaders of armies--could not cross the pomerium, the ritual boundary of the city (distinct from, and significantly smaller than, the actual city), it's that promagistrates could not do so. Not only could actual sitting magistrates enter the city (even with military forces) without surrendering either the army or their magistracy more generally, but in point of fact they did so rather frequently. Promagistrates, on the other hand, were typically created explicitly to exist outside the city, which was the place of the elected magistrates for the year. As such, a promagistrate who crossed the pomerium would be forced, legally, to surrender his imperium and with it his status as a promagistrate.

The most famous example of this being a problem was in 52, when the riots that occurred after P. Clodius' death delayed the elections for months, resulting in a string of interreges. An SCU was passed to allow the magistrates to deal with the problem, but unlike in 63, when Manlius' rebellion was safely away at Faesulae (although a bit too close for comfort, but at least not within the city itself), allowing the consuls to send people out to recruit troops, there was no opportunity to raise an army. Moreover, not only were there no magisterial armies in Italy in 52, because of the delay in the elections there were no magistrates at all. All that was available was Pompey's army outside the city. But Pompey, who had been consul in 55, was not a magistrate but instead a proconsul. As such, he could not enter the city. In order to allow Pompey to enter the city and at least get the ball rolling on returning the state to normal operation the senate voted, in a decision that no doubt Cinna would've had strong words about, to make Pompey sole consul for two months, which allowed him to deploy his troops within the city.