The non-dispensationalist develops a Biblical theology of the OT from a NT understanding of the OT text.
Mind telling me why you think it's a bad idea to pay attention to the way Jesus, Paul, the gospel writers, Peter, Jude, James and whoever it was who wrote Hebrews interpreted the Old Testament?
If you read the NT back into the OT, it is a trivial matter to impute to a passage a meaning that would not be gained from grammatical and historical associations. I.e., you can read into the passage whatever you want.
Instead of considering textual, grammatical, and historical factors as the primary instruments for interpretation, the non-dispensationalist considers theological factors of primary importance. The OT context is downplayed and gives way to the NT theological interpretation. I.e., by reading the NT back into the old, you minimize the OT background of the NT text ... and at the extremes dispense with it altogether.
By starting in the OT, the dispensationalist enhances and expands the NT understanding as he already has his Biblical theology of the OT in hand when he comes to the New. When you start in the New and read back into the Old, the tendency is to undo or replace the understanding that would have been had by constructing a true Biblical theology of the OT.