Urban legend, I'm afraid. Disclaiming addendum: with most people and most multimeters! The teacher probably just didn't want you spouting blood all over the classroom and equipment.
Let's look at why:
Using Ohm's law and a pessimistic 1000 ohms for the human, your multimeter would need to put 1000 ohms * 0.05A = 50V across its terminals.
Alternatively, for death by 9V, you'd need to have an internal resistance of 9V / 0.05A = 180 ohms
In other words, unless you're a very good conductor, you're safe.
Phssthpok - firstly, it is current, not amperage. Secondly, most multimeters test with DC, so you'd still be OK. Thirdly, the bits of the sinoatrial node that matter are small. Really small. To get 100mV potential difference across them, you'd have to apply 9V across just 90x their width, assuming homogenous resistance.