Was Peter a Steward of the Same Mysteries as Paul?

Let a man so account of us, as of the ministers of Christ, and stewards of the mysteries of God. (1 Cor. 4:1)

Some claim that because Peter was mentioned in 1 Cor. 3:22, that Paul also had Peter in mind in 1 Cor. 4:1. They think this proves Peter and Paul had the same ministry. The text does not specifically say that Paul had Peter in mind. The “us” goes back to 1 Cor. 3:4-5 (us = Paul and Apollos). Also, Paul said that the things he gave in a “figure” (laborer, builder, steward) applied to Apollos and himself (1 Cor. 4:6). He mentioned Peter in 1 Cor. 3:22 because of what he said back in 1 Cor. 1:12 (the carnal Corinthians were glorying in men, 3:21). Peter was a steward of the mysteries of the kingdom (Matt. 13:11), and he understood them (Matt. 13:51-52). Peter knew that God had given Paul a special ministry for this present age, but he confessed that didn’t fully understand the mysteries that Paul wrote about in his epistles (2 Pet. 3:15-16). How could Peter be a faithful steward of mysteries he didn’t understand? Also, in his epistles, Peter did not even mention the mysteries that Christ revealed to Paul (such as the Body of Christ and our rapture).