Don't misinterpret what the parent is saying. It's not "one introduction will", it's "one introduction could". If you are wealthy and connected enough there are many folks who will gladly ensure your children are taken care of, if for no other reason than to be connected to the parent/family.

An introduction might lead to a job, apprenticeship, or internship. It might lead to a partnership somewhere or the opportunity to invest in some way you would not normally have access to. Or it could open the door to further introductions and connections. Network effects are powerful things, and being introduced to the right node in the social graph can make all the difference.