I think it means more than just sharing a cab or partnering someone in a game of bridge. Here is the passage Hatch was referring to in that article (1 Cor 10:14-22, KJV):
 Wherefore, my dearly beloved, flee from idolatry.  I speak as to wise men; judge ye what I say.  The cup of blessing which we bless, is it not the communion of the blood of Christ? The bread which we break, is it not the communion of the body of Christ?  For we being many are one bread, and one body: for we are all partakers of that one bread.  Behold Israel after the flesh: are not they which eat of the sacrifices partakers of the altar?  What say I then? that the idol is any thing, or that which is offered in sacrifice to idols is any thing?  But I say, that the things which the Gentiles sacrifice, they sacrifice to devils, and not to God: and I would not that ye should have fellowship with devils.  Ye cannot drink the cup of the Lord, and the cup of devils: ye cannot be partakers of the Lord’s table, and of the table of devils.  Do we provoke the Lord to jealousy? are we stronger than he?
14 διόπερ, ἀγαπητοί μου, φεύγετε ἀπὸ τῆς εἰδωλολατρίας. 15 ὡς φρονίμοις λέγω: κρίνατε ὑμεῖς ὅ φημι. 16 τὸ ποτήριον τῆς εὐλογίας ὃ εὐλογοῦμεν, οὐχὶ κοινωνία ἐστὶν τοῦ αἵματος τοῦ Χριστοῦ τὸν ἄρτον ὃν κλῶμεν, οὐχὶ κοινωνία τοῦ σώματος τοῦ Χριστοῦ ἐστιν; 17 ὅτι εἷς ἄρτος, ἓν σῶμα οἱ πολλοί ἐσμεν: οἱ γὰρ πάντες ἐκ τοῦ ἑνὸς ἄρτου μετέχομεν. 18 βλέπετε τὸν Ἰσραὴλ κατὰ σάρκα: οὐχ οἱ ἐσθίοντες τὰς θυσίας κοινωνοὶ τοῦ θυσιαστηρίου εἰσίν;19 τί οὖν φημι; ὅτι εἰδωλόθυτόν τί ἐστιν; ἢ ὅτι εἴδωλόν τί ἐστιν; 20 ἀλλ’ ὅτι ἃ θύουσιν, δαιμονίοις καὶ οὐ θεῷ θύουσιν, οὐ θέλω δὲ ὑμᾶς κοινωνοὺς τῶν δαιμονίων γίνεσθαι. 21 οὐ δύνασθε ποτήριον κυρίου πίνειν καὶ ποτήριον δαιμονίων: οὐ δύνασθε τραπέζης κυρίου μετέχειν καὶ τραπέζης δαιμονίων. 22 ἢ παραζηλοῦμεν τὸν κύριον; μὴ ἰσχυρότεροι αὐτοῦ ἐσμεν;
koinonia, the abstract noun, in v. 16 (twice)
koinonos, a sharer or partner, in vv. 18 and 20.