I saw a presentation by a student in my department, where he's demonstrating k-fold cross validation using OLS.

He split the dataset $\mathcal{D}$ into k partitions as usual, and trained k OLS models on $\mathcal{D}\setminus \mathcal{D_k}$ and assessed the k-th model on the $\mathcal{D_k}$. So all of this so far is aligned with my understanding.

But then he made the statement that the model with the lowest prediction error is the chosen model, but he didn't train the "chosen" model on the entire $\mathcal{D}$ after performing k-fold CV. 

Is this procedure wrong? I thought you're supposed to train the chosen model on the entire dataset after performing cross validation?