My POV is pessimism. If I get an odd reading, I always assume I made a mistake and check again.
When starting a red wine or any fruit with lots of pulp, I make 3 checks in different parts of the must. If my readings differ by more than a point, I stir, then check again. The drill-mounted stirring rod makes this much easier.
I use a FermTech wine thief, which is wide enough internally to hold a hydrometer. I keep it clean and sanitize before use. Withdraw a sample, drop the hydrometer in, and take the reading. Sometimes I have to spin the thief to dislodge bubbles and/or to get the hydrometer away from the sides. Yeah, that can sometimes be a pain. When done, there is a pin on the bottom of the thief -- press that against the side of the fermenter or the inside of the carboy mouth, and the wine drains back in. This makes drawing the sample easy and it greatly reduces air contact.
Note -- this works great on carboys and barrels, but 4 liter jugs usually have too narrow of a mouth to fit.
Here is one source:
Fermtech Wine Thief