They stated that ICE is only going after “criminal” cases and not blanketing schools.
That's bullshit. If you want to go after criminals, there's a whole criminal justice system devoted to it. It's cheaper and easier for the federal government, and the feds get to run the identities of anyone who goes into the system anyway, and then snatch them if there's anything immigration-related they want them for. The only reasons to get ICE involved is if you want detailed control of the process, or you want it to go faster, or you want to grab people who have no other criminal issue. Currently, it's all three, and every single one of those is a big problem for the safety of the people involved.
They are lying to you, maybe because ICE is lying to them. But they're absolutely going to be grabbing people who haven't done anything wrong (not that committing a misdemeanor means that ICE should have you, anyway). If they were concerned about crime or violence, they wouldn't have just let 1500 criminals and violent criminals walk free.