I would say that Larry is right, but yet he isn't. If his 12V sources are a 12V, 10A regulated supply & a 12V, 1A regulated supply, then, of course, he is right. If his sources are 2, 12V transformers, 1 a 10A, the other a 1A unit, the 10A transformer will flow more current through the load. This is naturally the case because we know that the output voltage of the 10A TX will be more than that of the 1A TX when they are both loaded at 1 Amp.

When we design linear supplies we consider how they can handle their maximum load conditions. But we also have to consider them under no or minimal load conditions, watching for excessive voltages on the input filter.
Joe