If you are not my client then I will happily poach your people till you have none left.
If you are my client, then I will only find a job for your employees if the employee in question has already left the company, or if the client has explicitly said to me "can you find a job for this employee who has left us?"
Rules - there's rules for how to behave with integrity.
> If you are not my client then I will happily poach your people till you have none left.
That was his point, as soon as your client is no longer your client you poach their engineers on behalf of your new clients. It might not work exactly like that with you, but I bet a lot of recruiters have no moral qualms about poaching from an ex-client.
I see nothing wrong with this. Employers are not entitled to their employees. While bad employers moan about getting poached, good employers make sure that their employees have meaningful reasons to stay.
In sectors with no such pressure, employees have to pee in bottles just to shave a little bit of productivity.
Employees don't leave because a head hunter made them leave.
They leave because they want to leave. Because someplace else offered them a job that they think will be better, be it pay, work environment, commute, work/life balance, or some other factor(s).
Recruiters and head hunters just helped the ex-employee find out about a job that will, potentially, make them happier.
That means when your recruiter will leave - he\she will take your employees along