Matthew 28:16-20 we see Christ laying out the Great Commission just before his Glorious Ascension into Heaven. Jesus is sending out His Church to go to all the nations administering Baptism and to teach what He commanded them. This is not Christ alone, but it is through Christ's Church that His word is being proclaimed.
Ephesians 3:1-4 St. Paul is clear that he was made an apostle, not for his own ego, but for our benefit. Again, it is not Christ alone, but it is through Christ that St. Paul became an apostle and this includes all who have been ordained in the Catholic Faith! Consider 1 Timothy 4:11-16, 2 Timothy 1:6, and Titus 1:5 which the doctrine of Apostolic Succession is recognized.
James 5:13-17 addresses the Anointing of the Sick, here St. James call for the sick to call for the priest who will offer this great Sacrament of healing through the Church. The purpose of conducting and administering this duty was built into the Ministry of the Church by Christ Himself. The result shows healing and forgiveness to the sick. Again, it is not Christ alone, but it is through Christ this is accomplished.
The real teaching from Scripture is clear over and over again, Christ is the Mediator between God and man, but the truth is this: The Virgin Mary, the Saints, the Catholic Church, her Sacraments, Scriptures, Tradition, all of it works as a result of Jesus Mediation. That is the bottom line.
The basic problem with "In Christ Alone" and Jesus as "Mediator" is that those making this challenge, are attacking the Catholic authority, for them it is "Bible alone"? So for them, "In Christ Alone", it is really their imposing what it means to them, their own personal interpretation?