Current is not pushed, current is pulled or drawn.
If the motor is rated at 160 mA stall current, and the h-bridge or driver can supply up to 227 mA of current, that leaves a margin of current supply of about 42% (if my math is correct), which should be adequate. If the current pulled by the motor somehow exceeded that of the driver (here at 227 mA), you would smoke the driver; but, if given that the motor really has a stall current of 160 mA, you won't exceed the current delivery capability of the driver (now then, the driver may warm up, or possibly overheat, and hopefully it will have a automatic shutdown to keep that from happening; if not, you will need to find some way to deal with that extra heat to keep the driver cool).
Regarding your question on chinese toys - it's called economies of scale (that, and bad or misleading labeling, I would imagine)...