When "If $A$ is true then $B$ is true", is it valid to assert that "If $B$ is false, $A$ must also be false"?
I think the problem OP has is that the statement given is about propositional(zero-order) logic but to solve his confusion he will need predicate(first-order) logic, i.e. both "people"s in the statement means all people by the author. Because clearly there are some people, in real world, that don't ride planes, but ride buses. You may take a look about predicate logic.
When you say people, you should be clear about what you meant:
People that ride buses, also ride planes: Do you meant all people? If this is the case then you're saying $$\forall x, P(x)\to Q(x), x=\textrm{people}.$$
Since there are some people in the world that "don't ride planes, but ride buses" but that's your another problem: When someone say
$$\textrm{If}\ A\ \textrm{then}\ B,$$
in your case $A:$ (all) people that ride buses. "$A$" don't have to be true in read world. What this logical statement(assumed true) means is that $B$ must be true when I suppose $A$ true.
Notice that when you interpret $A$ as
$$\exists x, P(x)\to Q(x),$$
in your case $P(people)=$ some people ride buses; $Q(people)=$ they(same people) also ride planes.
Then yes the conclusion
$$\forall x, \lnot Q(x)\to \lnot P(x), (\textrm{which is }\equiv(\forall x, P(x)\to Q(x))),$$
is false because this is stronger then the original one. You implicitly changed $\exists$(exists) to $\forall$(for all) in your brain, but that's fine because when we doubt a thing we will be trying to find the counter example implicitly. That's why we extend the propositional logic to predicate logic, because the latter is more precise.
The difference lies in the logical statement
If $A$ is true, then $B$ is true.
Which is distinct from
(The truth value of) $A$ implies $B$.
You need to go beyond the examples you can provide with colloquial English, since a statement like
It is raining implies it is cloudy.
Has an exception, since "sun showers" exist.
Now, you're meant to regard $A \implies B$ as an agreement. The agreement being
The statement $A \rightarrow B$ is true, and so is the statement $A,$ then we agree that $B$ is true (this is modus ponens).
If you accept this statement, then you can derive the contrapositive: which is that $A \implies B$ is true precisely when $\neg B \implies \neg A$ is true.