The prof agrees that it probably refers to the church. However, he notes that the church gets its life from the Word of God and sees the church as a support (pillar) for the truth in a subsidiary (subordinate) sense to the word, which is the foundation. So in short, he believes that it is both - God and the Church, as God's subordinate.
If you look at the consistant use of the word "house" in the text it means "household" or "family" not a place or institution. What Paul is talking about is the local family of God, especially since there were many local representations of the "household of faith". It was in the local "household", the assembly or company of those called out by the Holy Spirit, that the truth, the the word of God, was maintained and propagated by the Holy Spirit through the gifts given to the local household of faith.
Very true. It remains a prooftext against scripture divorced from the Church as pillar and foundation of truth, my original point.