When is it permissible to use the stoichiometry of a reaction to determine rate laws?
Your reasoning is correct. When the reaction you are investigating is an elementary reaction step, you can write down the rate law using the stoichiometry of the reaction. Mathematically, this is done as follows.

Consider a reaction as

$$
\sum_{i} \nu_{i} R_{i} \rightarrow \sum_{j} \nu_{j} P_{j}
$$

Where $R$ and $P$ are reactants and products respectively and $\nu_{i}$ and $\nu_{j}$ are the stoichiometric coefficients.

If this reaction is an elementary reaction step, than the rate law in the forward direction is given by:

$$
r = k \prod_{i} [R_{i}]^{\nu_{i}}
$$

where $[R_{i}]$ is the concentration of reactant $R_{i}$ and $k$ is the rate constant.

For example, if you consider the reaction

$$
A + 2B \rightarrow 3C,
$$
then the rate in the forward direction is

$$
r = k[A][B]^{2}.
$$