Other than very rare situations (such as a government installation), you're probably correct: the property owner can't force you to submit to a search, all they can do is deny you access to their property or kick you off their property.
However, if you consent to being searched as part of the conditions of employment, your employer can fire you for refusing to consent to a search. Generally speaking, your employer can demand that you consent to a search on the spot, even if no previous rule existed to that effect. If you refuse, he can fire you.
Wrong, 18USC241 forbids it. He can not extort someone to surrender their rights. He is limited to firing them w/o cause, or just make some bogus statement.
"Generally speaking, your employer can demand that you consent to a search on the spot, even if no previous rule existed to that effect. If you refuse, he can fire you."
Or I can park elsewhere. My boss expects me to be armed, he might fire me if I refused to carry my gun...hahaha!