Metacatholic in this post notices a missing word from the statement (actually, as you will see if you click on the link, Metacatholic works off another post).
That word is 'interpretation', in connection with understanding Scripture.
It's quite important!
If X says I believe in Scripture and submits to its authority; and Y says I believe in Scripture and submit to its authority; and X and Y disagree theologically, then their disagreement is not solved by impugning their lack of adherence to Scripture. It is solved by sorting out their difference in the interpretation of Scripture.
And conservative evangelicals know sorting such difference is not easy.