Most places cut off the lock of the owner and put their own lock. Some places in addition put on a little one-use breakaway tag. It all depends on the laws in your state. I would say 90% or more of the storage places you go to do not go into or through the unit. They just pop the lock, do a sight inventory the way you do, and then put their lock and tag on. One place near me takes a picture w/ a piece of paper showing the date, location, name on unit, and unit #. Each facility is a little different.
You will quickly learn if a place is know to either stage units or search them. If you go to a place that many of the regulars don't go to and it's the only auction going on that day...that can be a clue. If the unit is old with dust covering most items but you see clear spots that can clue you in. If every box you see looks to be open, tape (if taped) cut, etc. that can be a clue. Many times it's the owner that has come in and grabbed what they want and discarded the trash. Very few times is it the facility.
It only takes 1 bad apple to give the whole industry a bad wrap. For myself I've not had a problem like this. But I keep my eyes and ears open.