33 I have coveted no man’s silver, or gold, or apparel.
34 Yea, ye yourselves know, that these hands have ministered unto my necessities, and to them that were with me.
No, it does not. A common mistake is to take a particular situation or statement by one person and attempt to apply it as a rule to all situations. All this passage means is that Paul worked to provide for his own living while he lived among the Ephesians. Paul did accept provision from others in other cities and at other times. The book of Philippians is in many ways a thank you letter for gifts given.
He speaks to this again in his first letter to the church in Corinth:
So, no, this is not a universal principle that no one should ever receive his living from those to whom he ministers. It merely records that a minister does not have to do this, and Paul, in particular, did not do this during one specific place in his ministry, though he did receive compensation elsewhere.