How do they stop him? It sounds like "can't access the data" means "the rules say he cannot access it, and if he is caught he'll get in trouble." Given that the people we are talking about think in terms of "the least untruthful statement" they can make, I would demand as much detail as possible.
"I don't have that much of a problem with this because the warrant is needed in order to actually do anything with the information."
Today a warrant is needed. Tomorrow, maybe not. What if tomorrow, the law changes, and the government starts hunting down anyone with leftist leanings? The first thing they'll do is query the database.
Laws are not sacred. Laws can be ignored or changed at any time. When we have to worry that the list of people we speak with today might be used against us tomorrow, there is a chilling effect on free speech. That is the danger of these databases. It is not enough that the data is held but can only be touched with a warrant; the data should not exist without a warrant.