The web browser is still run with its output and input connected to your terminal.
Disown will only stop your shell from sending signals to it when it sends signals to its children.
To get rid of the output you need to redirect the output
browser > /dev/null 2>&1 &
or
browser > /dev/null 2> /dev/null
If you are running this in an ssh session you will also want to disconnect the input just in case so that it does not hang:
browser < /dev/null > /dev/null 2>&1 &
and then you can also disown it
browser < /dev/null > /dev/null 2>&1 &
disown