tl;dr: The recommendation is likely driven from you and the provider adding each other to a contacts app LinkedIn has been authorized to source connection data from.

The "People You May Know" feature on LinkedIn is powered by a combination of:

- network analysis (you know A, B, and C. they all know D. you may know D.)

- mining data from your mobile address book (you have A in your contacts, A has you in their contacts, you may know A.)

The recommendation likely occurred as a result of you and the provider adding each other as a contact in a contacts app each of you have authorized LinkedIn to access.