Just say yes and move on to another question (or followup why that is relevant)
In all aspects relevant for the job, your current status is equal to literally owning a car. So while you would be technically lying, the moral implications are inexistant. Especially to a shady LinkedIn recruiter.
Don't get caught up in some dodgy-sounding half-answers that are just weird ways of saying no. The recruiter asks a bs question so they get a corresponding answer.