The "official" status of superhero teams tends to vary pretty wildly. For instance, the Avengers (and by extension, S.H.I.E.L.D.) are honored as official protectors of the world, and the government is happy to consult with teams like the Fantastic Four. Other teams, most notably The X-Men, are often feared by the public or, at best, seen as vigilantes mucking about in things they shouldn't. Given the makeup of the team, it seems highly likely that the Netflix Defenders will be in the latter position, but this hasn't always been the case with their comics counterparts.
Once upon a time, the comics Defenders worked for the government—or at the very least, they had government clearance. They once fought the awesomely-named Secret Empire while many of Earth's better-known heroes were away during the original Secret Wars crossover event. At the end, the good guys won, and for their efforts, they were honored with official government clearance. This particularly pleased the Beast, who wanted this infamous "non-team team" to be more official. And while cynics might note that Secret Wars sucking away all of the better-known heroes may have influenced the government's decision, it's interesting to note that, for a time, this group of "outsiders" were actually organized, official protectors of the nation.