Comments on your two sentences quoted.
The first is partially correct.
The second is not.
Details below.

The mid-field Customs facility in the C Concourse is used by all TRANSFERing international-arriving passengers on United and most of their Star Alliance partners (including LH OS SK NH ET SN SA). If you are transferring through Dulles on any of these international-arriving airlines flights, you are directed to the TRANSFER customs facility (mid-field facility) - which is where your checked bags will be delivered.

If you arrive on UA and making a connection (ANY connection), you de-plane at a C gate; walk a sterile walkway; go down two escalators to the ground-level immigration/customs/bag recheck/TSA facility; up an escalator into the C Concourse by gate C7; go to your connecting gate. If you are not connecting, you get on a mobile lounge at the end of the sterile walkway that takes you to the IAB facility in the Terminal building.

If you arrive on another Star Alliance airline mentioned above and making a connection (ANY connection), you de-plane at an A or B gate; walk a sterile walkway; and get on a mobile lounge that takes you to the mid-field facility. If you are NOT connecting, you get on a different mobile lounge that takes you to the IAB facility in the Terminal building.

Notes in reference to UA and Star Alliance international arrivals where checked bags are tagged for the final destination:
(a) If you have checked bags, they are directed to the customs facility that YOU are supposed to go to (ARRIVALS at IAB, or TRANSFERS in the mid-field C concourse). If you go to the wrong customs facility, the airline has to clear your checked bags through customs and get them back to you at their baggage office in the Terminal - that can take a fair amount of time.
(b) If you are connecting through Dulles (signs say TRANSFER), it doesn't make ANY difference whether your connecting flight out of Dulles is domestic or international - and it doesn't make ANY difference what airline you are connecting to - you should go to the mid-field customs facility where your checked bags will be sent.
(c) Several Star Alliance airlines do NOT do the customs split at Dulles - all their passengers go to IAB in the Terminal building. These include TA, CM, AV, and TK.

(I work at Dulles and am inside both Customs facilities every week.)