Regarding Gary Seven, I've always seen him as more Klaatu than Doctor Who. It seems to me that The Day The Earth Stood Still
is to "Assignment: Earth" as Forbidden Planet
is to Star Trek.
Granted, there's no way to know for sure that Roddenberry was thinking of Klaatu when he invented Gary Seven, but the characters seem to be cut from the same cloth. They're both somewhat austere, dignified visitors from a more advanced civilization whose missions are to save mankind from itself. Even their speech patterns and mannerisms are similar, and they both have the same sort of rueful bemusement at the "primitive" society they've come to save. And they both find themselves requiring the assistance of an ordinary Earthwoman, who is a little freaked-out at first, but who eventually rises to the occasion . . . .
And, yeah, the line about time-travel probably served two purposes on the Trek episode: it generated some uncertainty and suspense about Seven's origins, in order to justify Kirk's suspicion of him, and it also kept their options open if and when Gary Seven got his own tv series.
Like Christopher, I doubt that "Assignment: Earth: The TV Series" would have centered
around time-travel like "Doctor Who," and that most of the time he and Roberta would've been running around protecting the 20th Century, but, yeah, why not leave yourself the option to do a time-travel ep once and while, just like Trek did?