1Then a number of bhikkhus approached the Blessed One … and said to him: sn.iv.51 "Here, venerable sir, wanderers of other sects ask us: ‘For what purpose, friends, is the holy life lived under the ascetic Gotama?’ When we are asked thus, venerable sir, we answer those wanderers thus: ‘It is, friends, for the full understanding of suffering that the holy life is lived under the Blessed One.’ We hope, venerable sir, that when we answer thus we state what has been said by the Blessed One and do not misrepresent him with what is contrary to fact; that we explain in accordance with the Dhamma, and that no reasonable consequence of our assertion gives ground for criticism." [n.44] A stock passage in the Nikāyas, recurring in SN in slightly different forms determined by the context, at SN12.25, 12:26, SN22.2, 22:86, SN35.81, 42:13, SN44.2, and SN45.5. The readings alternate, even within the same volume, between vādānuvādo and vādānupāto, and it is uncertain which of the two is more original. The passage has stumped previous translators, mainly because of the phrase koci sahadhammiko vādānupāto, which at KS 2:28 is rendered "one who is of his doctrine, a follower of his views." To avoid such errors two meanings of sahadhammika must be distinguished: (i) a noun meaning a follower of the same doctrine (unambiguously so at MN11 (MN I 64,13)); and (ii) an adjective meaning legitimate, reasonable (unambiguously so at SN41.8 (IV 299,25 foll.)). Here the second meaning is applicable.
Spk explains: "How (should we answer) so that not the slightest consequence or implication (vadanupato vadappavatti) of the ascetic Gotama's assertion—(a consequence) which is reasonable because of the reason stated (vutta-karaṇena sakaraṇo hutva)—might give ground for criticism?" This is meant: "How can there be no ground for criticism in any way of the ascetic Gotama's assertion?" I dissent from Spk on what is to be safeguarded against criticism: Spk takes it to be the Buddha’s assertion, while I understand it to be the inquirer's account of the Buddha’s assertion. In other words, the inquirer wants to be sure he is representing the Buddha’s position correctly, whether or not he agrees with it.
At AN5.5 (AN III 4,10, 19) sahadhammikā vādānuvādā gārayhā ṭhānā āgacchanti occurs in a context where it means simply "reasonable rebukes, grounds for criticism, come up," and is contrasted with sahadhammikā pāsaṁsā ṭhānā āgacchanti, "reasonable grounds for praise come up."

2"For sure, bhikkhus, when you answer thus you state what has been said by me and do not misrepresent me with what is contrary to fact; you explain in accordance with the Dhamma, and no reasonable consequence of your assertion gives ground for criticism. For, bhikkhus, it is for the full understanding of suffering that the holy life is lived under me.

"But, bhikkhus, if wanderers of other sects ask you: ‘What, friends, is that suffering for the full understanding of which the holy life is lived under the ascetic Gotama?’—being asked thus, you should answer them thus: ‘The eye, friends, is suffering: it is for the full understanding of this that the holy life is lived under the Blessed One. Forms are suffering … Whatever feeling arises with eye-contact as condition … that too is suffering … The mind is suffering … Whatever feeling arises with mind-contact as condition … that too is suffering: it is for the full understanding of this that the holy life is lived under the Blessed One. This, friends, is that suffering for the full understanding of which the holy life is lived under the Blessed One.’ sn.iv.52

"Being asked thus, bhikkhus, you should answer those wanderers of other sects in such a way."

1Atha kho sambahulā bhikkhū yena bhagavā tenupasaṅkamiṁsu … pe … ekamantaṁ nisinnā kho te bhikkhū bhagavantaṁ etadavocuṁ: "idha no, bhante, aññatitthiyā paribbājakā amhe evaṁ pucchanti: ‘kimatthiyaṁ, āvuso, samaṇe gotame brahmacariyaṁ vussatī’ti? Evaṁ puṭṭhā mayaṁ, bhante, tesaṁ aññatitthiyānaṁ paribbājakānaṁ evaṁ byākaroma: ‘dukkhassa kho, āvuso, pariññātthaṁ bhagavati brahmacariyaṁ vussatī’ti. Kacci mayaṁ, bhante, evaṁ puṭṭhā evaṁ byākaramānā vuttavādino ceva bhagavato homa, na ca bhagavantaṁ abhūtena abbhācikkhāma, dhammassa cānudhammaṁ byākaroma, na ca koci sahadhammiko vādānuvādo gārayhaṁ ṭhānaṁ āgacchatī"ti?

2"Taggha tumhe, bhikkhave, evaṁ puṭṭhā evaṁ byākaramānā vuttavādino ceva me hotha, na ca maṁ abhūtena abbhācikkhatha, dhammassa cānudhammaṁ byākarotha, na ca koci sahadhammiko vādānuvādo gārayhaṁ ṭhānaṁ āgacchati. Dukkhassa hi, bhikkhave, pariññātthaṁ mayi brahmacariyaṁ vussati.

Sace pana vo, bhikkhave, aññatitthiyā paribbājakā evaṁ puccheyyuṁ: ‘katamaṁ pana taṁ, āvuso, dukkhaṁ, yassa pariññāya samaṇe gotame brahmacariyaṁ vussatī’ti? Evaṁ puṭṭhā tumhe, bhikkhave, tesaṁ aññatitthiyānaṁ paribbājakānaṁ evaṁ byākareyyātha: ‘cakkhu kho, āvuso, dukkhaṁ, tassa pariññāya bhagavati brahmacariyaṁ vussati. Rūpā … pe … yampidaṁ cakkhusamphassapaccayā uppajjati vedayitaṁ sukhaṁ vā dukkhaṁ vā adukkhamasukhaṁ vā tampi dukkhaṁ. Tassa pariññāya bhagavati brahmacariyaṁ vussati … pe … mano dukkho … pe … yampidaṁ manosamphassapaccayā uppajjati vedayitaṁ sukhaṁ vā dukkhaṁ vā adukkhamasukhaṁ vā tampi dukkhaṁ. Tassa pariññāya bhagavati brahmacariyaṁ vussati. Idaṁ kho taṁ, āvuso, dukkhaṁ, tassa pariññāya bhagavati brahmacariyaṁ vussatī’ti.

Evaṁ puṭṭhā tumhe, bhikkhave, tesaṁ aññatitthiyānaṁ paribbājakānaṁ evaṁ byākareyyāthā"ti.

Aṭṭhamaṁ.