Rank of matrix with full-rank submatrices

Question

Let us consider a matrix $X = [X_1, X_2]$ where both $X_1$ and $X_2$ are of full column rank. When $M_{X_1}X_2 \neq 0$ holds where $$M_{X_1} := I - X_1 (X_1'X_1)^{-1} X_1'$$ can we say that $X = [X_1, X_2]$ has full column rank? Or are there any counter examples?