ps -ad output unexpected

Based on the manpage, I'd have expected ps -ad be an union of processes in ps -a and ps -d. But I actually get more processes than that, for example this one now shows up:

$ ps -a -d -o pid,sid,tty,user,command
    PID     SID TT       USER     COMMAND
    199     199 hvc0     root     /sbin/agetty -o -- \u --noreset --noclear --keep-baud 115200,57600,38400,9600 - vt220

It sounds like plain ps -a only picks processes by the invoking users (which itself doesn't seem to match the manpage?) and then adding -d is lifting that restriction from -a.