I agree with you.
It's in the definition of the word "preach". The "Great Commission" of Matt 28 said "go and make disciples" Matt 24:14 said "the good news would be preached"
Later on when discussing spiritual gifts in 1 Cor. Paul said "some as teachers, some as. . " suggesting that as you say not all were gifted as evangelisers, preachers or public speakers but everyone had a gift to use.
St Francis of Assisi (sp?) is reputed to have said "preach the gospel wherever you go. If necessary use words"