I think you may be reading too much into the phrase "meat to hand". Like the English word "flesh" the Pali "maṃsa", by itself, may refer either to the flesh on a living animal or to meat from a dead animal. If one needs to disambiguate, then "alla-maṃsa" is used for living flesh and "pavatta-maṃsa" for dead meat. Now "meat to hand" is simply I.B. Horner's rendering of "pavatta-maṃsa". And so the passage doesn't carry any implication, say, that Sīha already had meat stored in his larder. The point of stipulating "pavatta-maṃsa" is to spell out that Sīha was sending the man to get meat from an animal already dead, as opposed to commissioning an act of butchery.
On rejection of human flesh
Then the Lord, having stayed at Rājagaha for as long as he found suiting, set out on tour for Benares. In due course, walking on tour, he arrived at Benares. The Lord stayed there near Benares at Isipatana in the deer-park. Now at that time in Benares the lay-follower, Suppiya, and the woman lay-follower, Suppiyā, were both pleased; they were benefactors, servitors, supporters of the Order. Then the woman lay-follower, Suppiyā, having gone to the monastery, having approached dwelling-place after dwelling-place, cell after cell, asked the monks: “Who, honoured sirs, is ill? What may be conveyed for whom?”
Now at that time a certain monk had drunk a purgative. Then that monk spoke to the woman lay-follower, Suppiyā, thus:
“I have drunk a purgative, sister. I need meat-broth.” She said:
“Very well, master, it shall be conveyed (to you),” and having gone to her house, she enjoined a servant, saying:
“Go, good fellow, find meat that is to hand.”
“Yes, lady,” but that man, having answered the woman lay-follower Suppiya in assent, touring the whole of Benares, saw no meat that was to hand. Then that man approached the woman lay-follower Suppiyā; having approached the woman lay-follower Suppiyā, he spoke thus: “There is no meat, lady, that is ready to hand; today is a non-slaughter (day).”
Then it occurred to the woman lay-follower, Suppiyā: “If that ill monk is unable to obtain meat-broth his affliction will greatly increase or he will pass away. It is not fitting in me, that I, having answered him in assent, should not have meat-broth conveyed”, and having taken a butcher’s knife, having cut flesh from her thigh, she gave it to a slave-woman, saying:
“Come now, having prepared this meat—in such and such a dwelling-place there is an ill monk, you may give it to him, and if anyone asks for me, let it be known that I am ill,” and having wrapped her upper robe round her thigh, having entered an inner room, she lay down on a couch.
Then the lay-follower, Suppiya, having gone to the house, asked the slave-woman, saying: “Where is Suppiyā?”
“She, master, is lying down in an inner room.” Then the lay-follower Suppiya, approached the woman lay-follower Suppiyā, and having approached he spoke thus to the woman lay-follower Suppiyā:
“Why are you lying down?”
“I am ill,” she said.
“What is your affliction?” Then the woman lay-follower Suppiyā told this matter to the lay-follower Suppiya. Then the lay-follower Suppiya, thinking: “Indeed, it is marvellous, indeed, it is wonderful, that this Suppiyā is so faithful and believing that she gives up even her own flesh. What other thing could there be that she would not give?” and joyful, elated, he approached the Lord; having approached, having greeted the Lord, he sat down at a respectful distance.
As he was sitting down at a respectful distance the lay-follower Suppiya spoke thus to the Lord: “Lord, may the lord consent to a meal with me on the morrow together with the Order of monks”. The Lord consented by becoming silent. Then the lay-follower Suppiya, having understood the Lord’s consent, rising from his seat, having greeted the Lord, departed keeping his right side towards him. Then the lay-follower Suppiya, towards the end of that night, having had sumptuous solid foods, soft foods, prepared, had the time announced to the Lord, saying: “It is time, Lord, the meal is ready”. Then the Lord, dressing in the morning, taking his bowl and robe, approached the dwelling of the lay-follower Suppiya; having approached, he sat down together with the Order of monks on the appointed seat.
Then the lay-follower Suppiya approached the lord; having approached, having greeted the Lord, he stood at a respectful distance. As the lay-follower Suppiya was standing at a respectful distance, the Lord spoke thus to him:
“How is Suppiyā?”
“She is ill, Lord.”
“Well then, let her come.”
“She is not able to do so, Lord.”
“Well then, having taken hold of her, bring her along.” Then the lay-follower Suppiya, having taken hold of the woman lay-follower Suppiyā, brought her along. When the Lord saw her, even that great wound became healed, the skin was (made) good with (small) hairs growing on it.
Then the lay-follower Suppiya and the woman lay-follower Suppiyā, saying: “Wonderful indeed, marvellous indeed are the great psychic power and the great potency of the Truth-finder, inasmuch as when the Lord sees (someone) even a great wound will be healed, the skin (made) good with (small) hairs growing on it,” and joyful, elated, having with their own hands served, and satisfied the Order of monks with the enlightened one at its head with sumptuous foods, solid and soft, when the Lord had eaten and had withdrawn his hand from the bowl, they sat down at a respectful distance. Then the Lord having gladdened, rejoiced, roused, delighted the lay-follower Suppiya and the woman lay-follower Suppiya with talk on dhamma, rising from his seat, departed.
Then the Lord on this occasion, in this connection, having had the Order of monks convened, questioned the monks, saying: “Who, monks, asked the woman lay-follower Suppiyā for meat?” When he had spoken thus, that monk spoke thus to the Lord:
“I, Lord, asked the woman lay-follower Suppiyā for meat.”
“Has it been conveyed (to you), monk?”
“It has been conveyed, Lord.”
“Did you, monk, make use of it?”
“I, Lord, made use of it.”
“Did you, monk, inquire about it?”
“I, Lord, did not inquire about it.”
The enlightened one, the Lord rebuked him, saying: “How an you, foolish man, make use of meat without having inquired about it? Foolish man, human flesh has been made use of by you. It is not, foolish man, for pleasing those who are not (yet) pleased …” And having rebuked him, having given reasoned talk, he addressed the monks, saying:
“There are, monks, people who are faithful and believing; even their own flesh is given up by these. Monks, you should not make use of human flesh. Whoever should make use of it, there is a grave offence. Nor, monks, should you make use of flesh without inquiring about it. Whoever should (so) make use of it, there is an offence of wrong-doing.”