The year the episodes take place is 2024, just about 15 years in our future. I'm not sure if we are headed in that direction, however, one never knows what the future holds in store. One could make an argument that a situation like this is a very real possibility, espically if things keep on going the way that they are.
On a side note in DS-9 Little Green Men, while Quark and Rom are taking Nog to Earth, Nog had recieved a PADD with facts about Earths history. He happens to find the section on The Bell Riots, and the picture is that of Capt Sisko, who, if you recall had to take the place of the real Gabrial Bell.
When he mentions that the picture look just like Sisko, Quark says all Humans look alike...