Under the Han Dynasty, iron and salt were indeed vital resources for the economy and daily life. The state established a monopoly on the production of these goods to control their distribution and ensure that they were used efficiently, as well as to generate revenue for the state.
However, it was not forbidden to trade them outside of China, as trade was an essential part of the Han economy, particularly along the Silk Road. Additionally, while there were restrictions on who could produce these goods (often state-controlled production), it was not the case that only wealthy merchants or only the emperor's family could own them. The state aimed to regulate production and trade to benefit the broader economy and ensure access for the population as a whole.
So, the correct point would be that the production of iron and salt was made a state monopoly.