The same goes with receiving a righteous man. Quite often you read in Paul's epistles how he would send Timothy or Titus to minister in his stead to the Corinthians or to some other church congregation. The congregation didn't know who these men were personally, but knowing that these workers were sent by the apostle Paul was good enough for them, and they received them as they would have received Paul himself. It's the same when your pastor isn't able to preach on a given Sunday, so he invites another brother to come and minister the Word. As a congregation you welcome and receive the message this brother brings because he was commended to you by your pastor.
I associate this passage with the one in Hebrews 13:1-2, "Let love of the brethren continue. Do not neglect to show hospitality to strangers, for by this some have entertained angels without knowing it." Sure, there are false brethren in the church, and you always have to be careful about trusting strangers. But when you recognize another brother or sister in Christ, it is a unique aspect of Christian love that we are ready to minister to them, even though we don't know anything else about them, simply because we share the bond of knowing Jesus Christ. You might meet someone randomly while waiting at the airport or while on jury duty. You find out they are also a Christian, and pretty soon you're sharing about this and that, and pretty soon you're saying, "I'll pray for you" to each other as you part ways. Total strangers, but you have a bond in Christ. It just sort of happens automatically. (And it's kind of fun to think that maybe God sends people our way who aren't really people, but angels in disguise, just to keep us wondering.)
Some of the missionaries you support are actually strangers to you. That is, they may be people you've never met in person, but you had heard of the faithful work they were doing on the field and wanted to support them. I'll bet you never really thought about that before. Jesus says you'll be rewarded for your faithfulness. And yet Jesus also says in our passage that you don't have to even minister to prophets and righteous men to be rewarded. Your service to the littlest disciple won't be overlooked, even if it's as simple as giving him or her a cup of cold water. If you give to anyone in the name of a disciple, that is, just because they are a disciple of Christ, you shall not lose your reward.