Were I in the BO’s position, unless the HO had cleared with me that the horse could get extra hay, I would be upset. I’ve seen enough hay bills to know that most hay purchases are planned to the bale.
That said, this horse needs. more. hay. As it’s already been stated, not every horse is fine and dandy with 1-2% of body weight of hay. It sounds to me that he goes out in the morning with 3 flakes (how much does each flake weigh?) in a paddock without much grass. If he scarfs that hay down in even 3-4 hours, and his owner doesn’t come out and give him his midday snack of 1-2 flakes, he will spend a good portion of the day with a stomach only sloshing acid around. Same with the overnight: if his hay is gone by 10pm and he doesn’t get more until 7am, again he’s spending a goodly time with stomach acid and nothing else in his belly.
The hay net sounds like a start; perhaps give him a couple of flakes loose to satisfy his immediate hunger, and a couple in the net to last overnight. ETA: if you are concerned about his (over)weight, I would drop his grain and swap to a vitamin/mineral supplement or ration balancer and increase his forage. I would also highly recommend either scoping for ulcers or the week of Ulcergard to test for results. His behavior screams ulcers, and would have me kicking, striking, and generally expressing my discomfort to the world as well.