How dangerous is DMA?

There is this news about reading the contents of DRAM by chilling it
down and transferring it to another machine. Of course this only works
if one gets physical access to the computer, and should be quite
difficult to do without getting noticed. I once heard that reading the
entire memory, once physical access has been gained, can be done with
a simple DMA-enabled device. Is this true? Is the memory DMA is
allowed to access restricted? If DMA-based memory readout is possible,
it should be a vastly greater risk than shock-freezing a laptop. I
tried Google, but DMA seems to be rarely discussed in connection with
security issues.