As you say, it is possible to get a false high reading because you are reading the sugar content in whatever it is on your fingers as well as in your blood.
I do not believe it is possible to get a false low reading for the same reason (something on your fingers is unlikely to bring the reading down). However, our meters are not 100% accurate. As
@Bluetit1802 mentions, if you get a reading which is unexpected, it is worthwhile repeating it. And, if the reading is unexpectedly high, it is worthwhile washing your hands before the repeat.
That said, it is possible to have a reading of 3.8. Some people find exercise, for example, could bring down their BG although some find otherwise and some types of exercise certainly push my BG up (don't try doing a scary, challenging climbing route if you are trying to reduce your BG).