It seems that the issue here is just a matter of terminology. You are insisting on a certain definition of consubstantiation and claiming that your church does not believe in consubstantiation by that definition. But the rest of us are using a different definition. I’ve always understood consubstantiation to mean that, after the consecration, both the bread and the body are present, rather than just the bread (as most Protestants believe) or just the body (as Catholics believe), and based on your link this is exactly what the Lutheran church teaches.
In the Solid Declaration of the Book of Concord of the Lutheran Confessions, this is stated of the Sacramental Union:
35 In addition to Christ’s and St. Paul’s expressions (the bread in the Supper is the body of Christ or the communion of the body of Christ), the following forms are also used: under the bread, with the bread, in the bread. With these words the papistic transubstantiation may be rejected and the sacramental union of the bread’s unchanged essence and Christ’s body may be shown. 36 In the same way, the expression “the Word became flesh” [John 1:14] is repeated and explained by the equivalent expressions “the Word … dwelt among us” [John 1:14]; likewise, “in Him the whole fullness of deity dwells bodily” [Colossians 2:9]; likewise, “God was with Him” [Acts 10:38]; likewise, “in Christ God was” [2 Corinthians 5:19], and the like. These show that the divine essence is not changed into the human nature. But the two natures, unchanged, are personally united. 37 Many eminent ancient teachers, such as Justin, Cyprian, Augustine, Leo, Gelasius, Chrysostom, and others, use this comparison about the words of Christ’s testament, “This is My body.” Just as in Christ two distinct, unchanged natures are inseparably united, so in the Holy Supper the two substances—the natural bread and Christ’s true natural body—are present together here on earth in the appointed administration of the Sacrament. 38 This union of Christ’s body and blood with the bread and wine is not a personal union (as that of the two natures in Christ). But Dr. Luther and our theologians, in the frequently mentioned Articles of Agreement ‹Formula Concordiae› in the year 1536 and in other places, call it a sacramental union. By this they wish to show that, although they use these distinct modes of speech: in the bread, under the bread, with the bread, yet they have received Christ’s words properly. They read, and have understood the proposition that the words of Christ’s testament (“This is My body”) are not a figurative, allegorical expression or comment, but are a unique expression. 39 Justin says:
This we receive not as common bread and common drink. We receive them as Jesus Christ, our Savior, who through the Word of God became flesh. For the sake of our salvation He also had flesh and blood. So we believe that the food blessed by Him through the Word and prayer is the body and blood of our Lord Jesus Christ.
referring to the Lutheran understanding of Christ “in, with, and under” the bread and wine.