Tentmaking?

I am reading Acts at the moment, and have just finished chapter 20. Paul is saying goodbye to the Ephesian elders; a touching story. What I really noticed was Paul’s statement in verse 34: “Yes, you yourselves know that these hands have provided for my necessities, and for those who were with me.” Other books I am reading claim that Paul only worked when absolutely necessary as an example to others, and was otherwise supported by the local church, allowing him to devote his time to teaching. This verse apparently refutes that, being seemingly general, not specific to one particular situation.
However, we see other situations in which the leaders of the church probably were ministering full-time, and supported by church members: in Acts 6:2, where the twelve called together the whole community of the disciples and said, “It is not right that we should neglect the word of God in order to wait on tables.” It is possible, of course, that they also worked, and simply said that it would make more sense for them to use what little remaining time they had on the word of God. However, we see no reference to their fishing boats in Acts, in contrast to the gospels, so it seems reasonable to assume that they were focused full-time on teaching the word of God, and supported by the church.