How does "The Last Leaf" illustrate that a loaf of bread is more preferable to the hungry than simply telling them to "be filled"?
Is it because the old artist actually went out and did something to try and let Johnsy live rather than just tell her to stay alive like Sue did?
I agree with your analysis, although I must admit I have never heard this saying about loaves of bread and the hungry.
What Behrman does "feeds" Johnsy's actual needs. He does not just sort of patronize her the way Sue does. Sue belittles her fears rather than taking them seriously. That is like telling someone to quit worrying about wanting bread.
By contrast, Behrman takes Johnsy seriously. He tries to help her, but on her own terms. He accepts her obsession with the leaf, even though he thinks she's being silly. By accepting her obsession, he is able to do something that actually does support her. That is why his help is more effective than Sue's.
Your analysis actually does work for this story. Johnsy, on her deathbed, is supported by her roommate, Sue. However, Sue mocks Johnsy's fixation with the last leaf on the vine, and tells her to snap out of it and focus on getting better. The gruff Behrman, however, does not say much of anything to Johnsy, and on the surface, might appear to be a bit insensitive about her illness and potential death. It is his actions, in the end however, that probably had the most impact on Johnsy's recovery. He didn't speak or give false comfort; he didn't mock her delusions (to her face at least), but instead fed her the hope and comfort that she needed in order recover from her illness.
As you mentioned above, if someone is starving, go out and get them bread, don't tell them to stop whining and get over it. So although Sue was there, helping Johnsy along the way, physically, she did not offer the crucial emotional support that Johnsy needed, which was hope. And even though it seemed ridiculous, and had nothing to do with recovery, Behrman went out and gave the poor girl the fulfillment of her clinging hope through the painting of the leaf. He gave her what she needed to recover.
I hope that those thoughts helped; good luck!