Living a quiet doesn't necessarily mean being a quiet person.
If we look at Paul's 1st and 2nd letter to the Thessalonians I think we get more context on what Paul means
1 Thessalonians 4:11
11 and to make it your ambition to lead a quiet life and attend to
your own business and work with your hands, just as we commanded you,
2nd Thessalonians 3:12
11 For we hear that some among you walk in idleness, not busy at work,
but busybodies. 12 Now such persons we command and encourage in the
Lord Jesus Christ to do their work quietly and to earn their own
In the 1st scripture he particularly says "your own business". Then in the 2nd scripture he is saying that people are walking around doing nothing, just busybodies, basically meaning meddlesome and in other people's business, and not being productive.
So instead quiet here means someone who minds their own work and not meddling in other people's affairs. (read this definition from the original greek: http://www.studylight.org/lex/grk/gwview.cgi?n=2271)
Now to contrast that we have this command from Christ:
19 Go therefore and make disciples of all the
nations, baptizing them in the name of the Father and the Son and the
Holy Spirit, 20 teaching them to observe all that I commanded you; and
lo, I am with you always, even to the end of the age."
We are supposed to go into the whole world and proclaim Christ, and that is the business we are to be about. ("I must be about my father's business" - Luke 2:49). I would say it is "business" versus "busyness"
So I think the key here is the definition of what Paul means when he says "quiet", which according to context isn't referring to silence.
So in short Billy Graham did what was right.
Now if Billy Graham was just a traveling meddler, that had no work of his own and just meddled in other people's stuff, he would've been wrong, but he was actually doing what Paul commanded, he was busy doing the work (the work of the Lord), and working with his own hands.