There have been two burglaries reported in the last week at open houses in our area.  One in particular in Northpark (not with my brokerage thank goodness!) was grand theft & resulted in several pieces of jewelry being stolen.

I cannot speak for other agents, but when I hold open houses, I tour the prospective buyers as opposed to allowing them to wander by themselves. I also ask for their name and number, as my first responsibility is my client's home and my own safety, and I need to know who they are.

Unfortunately, while most people comply, many do not and get upset when I ask them who they are or to please stick with me through the house.

Agents who hound open house visitors clearly are not helping the issue; no one likes to deal with pushy sales people. 

I'd humbly suggest that it is better for all involved to be open with the agent about who you are, follow the rules, and if the agent is not respecting you and badgering you, simply ask them to back off, or leave. For visitors who are rude and cagey as soon as they enter, if they had visited one of these homes prior to the burglary, chances are the agent is going to remember them, even if they had nothing to do with the theft.

For sellers, simply not doing open houses is of course an option. If you are going to do them- and depending on the area and the agent's skill level, they can be highly effective- making sure the agent you hire recognizes these issues & is capable of monitoring visitors is crucial.

Aaaand on that note...