If questioned, just indicate that you are waitlisting a United segment, not a partner segment. IME, it may take 2-3 more calls to reach an agent who understands this is completely possible.

Now, the only grain of truth to what the agent said is that if/when the segment clears, you will likely have to call to have an agent reissue the ticket, and I suppose a bad agent could do something stupid to the LH flights. IME, though, that would be very rare; on my most recent one, I had to have agents reissue at least three times (schedule changes plus cleared waitlists), and they preserved the partner flights without issue.