Backup power supply boost converter TPS61030
If you naturally set the output to regulate at 4.5 volts and a slightly higher voltage is present (due to Vsys and D1), the regulator will immediately shut-down it's output stage in order to try to regulate to 4.5 volts. Clearly Vsys holds the output higher at 4.5 volts hence the output stage of the regulator shuts down.


  those 4.5V should be also present at the output, lowering the value of
  the Vout when the Vsys is present


You have to remember that the output from this voltage regulator is not some kind of push-pull output that can force a lower voltage; it is a single series transistor between Vbat and Vout and will just go open-circuit when overdriven at its output.