house wired without separate ground - problem?

That's true.

In normal cases there are not enough current that can pass through the person body to cause a significant danger.

Even though the is a lot of current going on the neutral wire, the potential difference between the neutral wire and the "real" ground is quite low. Typically in normal operation (all wiring OK) up to few volts, transients to higher voltages.

When the voltage difference between ground and the neutral is just few volts, not much current can flow between a person that touches them both. The human body and skin has considerable resistance, especially on low voltages.

The dangerous voltage differences exist and dangerous currents can only flow when the neutral gets broken...

Wiring where grounded outlets gets only two wires (live and combinet neutral+ground) used to be quite common practice in several European countries (for example Finland) for a quit long time. At some point the regulations changed demanding separate neutral and ground wires to outlets in most cases.

-- Tomi Engdahl