Yes, your understanding is correct, although the reality of Washington politics means that it's unlikely to happen.
... under the current rules, any single house member can force a vote on removing the (Republican) House Speaker, including any Democrat.
Quoting from this article from when this happened to McCarthy last year (emphasis mine):
The motion to vacate is the House’s procedure to remove its speaker. The chamber’s current rules allow any one member, Democrat or Republican, to introduce the motion.
...
This was a change from the rules in place under [McCarthy's] Democratic predecessor, Nancy Pelosi, when a majority of one party needed to support a motion to vacate to bring it to the floor.
The reason this won't happen is a practical one. Under normal circumstances, the minority party could force a vote, but as discussed in this answer, there's no point when you can assume the majority will vote against it. After all, by definition they make up the majority of the House, which is enough to cause the vote to fail if they all vote together.
On the flip side, if you have members of the majority party who are willing to vote against the current speaker, then it's better for them to be the one to initiate the vote (for reasons that will sound good to their base) instead of just tagging along with the minority. After all, "supporting a Democratic motion" has very different optics from "taking a principled stance that just happens to have Democratic support".
So the only circumstances where the Democrats might expect to succeed in removing the speaker are when they have a commitment from enough Republicans to form a combined majority of their own, and as soon as you have that commitment, you now have a Republican who can raise the issue.