I worked for a company that carried continental freight, import/export. Unless the driver was complicit in this, it is virtually impossible for a driver to be unaware that the trailer has been accessed illegally. It's also inconceiveable that the 39 people weren't aware of the risks of travelling inside a refrigerated, solid-sided trailer. I believe this type of vehicle would have a lower priority for checking by officials due to the nature of its' composition. That's not to say they aren't checked. Some are, and it's easy to know when they have been because they are re-sealed with a customs seal. This applies more to containers than trailers. Drivers always check the seal after every stop, and before resuming their journey. If they find anything wrong, they have to follow their relevant procedures.
As I re-call, the BBC news said the 39 people were not from Europe, although that hasn't been confirmed. There's a lot more about this that we are probably not aware of, so anything else is just speculation. And I would guess from some people who know nothing about the workings of continental freight.