Your understanding is correct for many states; where police does not register FIR and the girl can move 498a as a private complaint case.
Here the procedure is:
Step 1: Complaint to the Court
Step 2: Pre-summoning evidence by the Complainant + her witnesses
Step 3: Summoning of the accused
Step 4: Evidence lead by Complainant + Witnesses
Step 5: Cross-examination
Step 6: Defence Evidence if any
Step 7: Arguments
Step 8: Judgment
The court can dismiss the complaint at Stage 2 itself; if it is not satisfied by the pre-summoning evidence led by the complainant and her witnesses.
If you don't fight for what you want, don't cry for what you LOST.