Jim...I think Ignatius should be required reading for anyone who believes they can characterize what "early Christians believed".
As for the phrase in question, here it is in its context:
"Flee from divisions, as the beginning of evils. You must all follow the bishop, as Jesus Christ followed the Father, and follow the presbytery as you would the apostles; respect the deacons as the commandment of God. Let no one do anything that has to do with the church without the bishop. Only that Eucharist which is under the authority of the bishop (or whomever he himself designates) is to be considered valid. Wherever the bishop appears, there let the congregation (pléthos) be; just as wherever Jesus Christ is, there is the catholic church (katholiké ekklesia). It is not permissible either to baptize or to hold a love feast without the bishop. But whatever he approves is also pleasing to God, in order that everything you do may be trustworthy and valid" (Ignatius, Smyrnaeans 8:1-2).
The main problem in interpreting the word katholiké is whether it has here its usual sense "universal" or the more technical sense "orthodox", which was dominant in third and fourth century AD texts. Since this was the first instance of the word in Christian literature, one could reasonably suppose a sense closer to the usual meaning. This was argued most clearly by JB Lightfoot in the 19th century and the lexicographical evidence shows that such universality was construed not in geographical terms but in terms of organic unity or completeness (as Schoedel phrases it). This builds on NT conceptions of the church (cf. also Didache 9:4, "Just as this broken bread was scattered upon the mountains and then was gathered together and became one, so may your church be gathered together from the ends of the earth into your kingdom"). The second-century gnostic Christians had a similar concept of the term; the adjective kotholikon denotes the "undivided" in the Treatise of Seth 57.26 in contrast to what is merikos "fragmentary". The context of the passage in Ignatius emphasizes the unity of the church from division, and the role of its leadership (the bishop, presbyters, deacons) in maintaining unity. The idea seems to be that holding meetings apart from the bishop puts one outside of the universality or totality of the church. If the word was used commonly in such a way, it is relatively easy to see how the later technical sense of "orthodox" arose.
Note also in this passage the contrast between the local congregation (pléthos), led by the bishop, and the whole church, led by Jesus Christ. This also confirms that the sense in this passage is closer to "entire church," "complete church," "universal church" than "orthodox" church. The idea is that holding separate meetings locally apart from the bishop is like designating a Christian church outside of the body of Christ (which should be the church in its entirety).