I have seen bettas that I cannot believe are still alive brought back from the brink and turn into beautiful, healthy creatures. So I would say no, there's not a point where treatment is cruel. If the betta dies, at least it wasn't abandoned in a dirty tank and devoid of love or proper care.
Bettas really need to be kept at a temp between 76-82 degrees, and for a stressed fish the temp should be around 80 to help boost the immune system. So if you don't have a heater in his bucket that could be contributing to him still being lethargic.
I highly recommend you get some Indian Almond Leaves, they are from a betta's natural habitat and the fish respond very well to them. Among other things, Indian Almond Leaves have antibiotic and calming properties, and can lower tank pH slightly through the release of tannins. They will stain water to be tea colored, which is what you want. They are safe to keep in the tank full time or just for treatment through a rough patch.
You can buy them online, but they take a really long time to ship from Thailand so I'd say try to find a US seller. I would offer you some of mine but I'm almost out and waiting on a shipment.
It's also quite normal for a new betta to refuse food for a few days, especially if the fish is already stressed out like this guy. As long as he's still pooping it's fine. Keep offering him one pellet every day. If he hasn't eaten it in 4-5 days he was probably fed something different before, so I'd either find out what they use or try a frozen bloodworm to see if that will get his appetite going.
I wouldn't use melafix or pimafix on a betta, just fyi. There's been too many reports of issues with it.
This is true. Anything ending in "-fix" should NEVER be used with a betta, even Bettafix (which is just watered down melafix). It will damage their labyrinth organ (the lunglike thing they use to breathe air).