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An opamp doesn't source any current.

You are wrong, Kevin.
ALL opamps have a NPN emitter-follower at the output to source current and an PNP emitter-follower transistor at the output to sink current.

Maybe you are thinking about the output of a comparator that does not have emitter-follower outputs so it is simply an NPN open collector that sinks current but needs a pullup resistor to source current. Then the outputs of many comparators can be connected together using a single pullup resistor which makes them an OR gate.

I corrected the above because I originally got it wrong.
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