Why can't you divide a series + parallel circuit into branches to get total current?
The circuit you analyse with your formula is essentially this one, with the switch open: two independent braches, each with two resistors in series.







simulate this circuit &ndash; Schematic created using CircuitLab

The current in the two braches is independennt, each current is V / ( R + R ). 

Note that the potential (voltage) at both sides of the switch is the same, so we can close the switch, without effect on the circuit. Now we have your circuit, except that R1 is represented by TWO parallel resistors, each R, so the equivalent is R/2.

To summarize, you analyzed your circuit as if it were the one I show, which is different from your circuit in the value of R1.

The comment from The Photon gives another view, which amounts to the same thing.