The earliest explanation in Vibhanga clearly states that 'parimukhaṃ' means the area at the tip of the nose (nāsikagge) or at the lip of the mouth (mukhanimitte):
"Parimukha.m sati.m upa.t.thapetvaa"ti tattha katamaa sati? Yaa sati anussati pa.tissati …pe… sammaasati - aya.m vuccati "sati". Aya.m sati upa.t.thitaa hoti supa.t.thitaa naasikagge vaa mukhanimitte vaa. Tena vuccati "parimukha.m sati.m upa.t.thapetvaa"ti.
Patisambhidamagga and Atthakatha explains 'mukha' as 'niyyāna' - "way out, outlet" (of the breath).
Parimukhaṃ satiṃ upaṭṭhapetvāti. Parīti pariggahaṭṭho. Mukhanti niyyānaṭṭho. Satīti upaṭṭhānaṭṭho. Tena vuccati – ‘‘parimukhaṃ satiṃ upaṭṭhapetvā’’ti.
Bhikkhu Sona quotes Patisambhidamagga-Atthakatha:
http://www.arrowriver.ca/dhamma/nimitta.html" onclick="window.open(this.href);return false;"Has the sense of embracing" is in the sense of being embraced. What is embraced? The outlet. What outlet? Concentration based on mindfulness of breathing is itself the outlet, right up to the arahant path. Hence "has the sense of outlet" is said. The meaning of "outlet from the round of rebirths" is expressed by the meaning of the word mukha (mouth) as foremost (front). "Has the sense of establishing" is in the sense of individual essence. The meaning expressed by all these words is: Having made mindfulness an embraced outlet. But some say that "has the sense of embracing'" stands for "embracing as the meaning of mindfulness," and that "has the sense of outlet" stands for "door of entry and exit as the meaning of in-breaths and out-breaths." Then what is meant is: Having established mindfulness as the embraced outlet of the in-breaths and out-breaths.(Note 14, Engl. Ed.; PsA 350-1)
"parimukha.m sati.m upa.t.thapetvaati kamma.t.thaan'aabhimukha.m sati.m .thapayitvaa. mukhasamiipe vaa katvaati attho. teneva vibha'nge vutta.m - "aya.m sati upa.t.thitaa hoti sіpa.t.thitaa naasikagge vaa mukhanimitte vaa, tena vuccati parimukha.m sati.m upa.t.thapetvaa"ti (vibha. 537). athavaa pariiti pariggaha.t.tho. mukhanti niyyaana.t.tho. satiiti upa.t.thaana.t.tho. tena vuccati- "parimukha.m satin"ti. eva.m pa.tisambhidaaya.m vuttanayenapettha attho da.t.thabbo. tatraaya.m sa'nkhepo- "pariggahitaniyyaanasati.m katvaa"ti.
However the article in Pali-English dictionary, referring to the same Patisambhidamagga passage states that:
Parimukha (adj.) [pari+mukha] facing, in front; only as nt. adv. ˚ŋ in front, before, in phrase parimukhaŋ satiŋ upaṭṭhapeti "set up his memory in front" (i. e. of the object of thought), to set one's mindfulness alert Vin i.24; D ii.291; M i.56, 421; S i.170; A iii.92; It 80; Ps i.176 (expld); Pug 68; DA i.210. Also in phrase ˚ŋ kārāpeti (of hair) Vin ii.134 "to cut off (?) the hair in front" (i. e. on the breast) Vin. Texts iii.138, where is quoted Bdhgh's expln "ure loma -- saŋharaṇaŋ."
Perhaps the error is due to explanation of Buddhaghosa, mentioned in the article:
'Parimukhanti ure lomasa.mhara.na.m'
(Parimukhaṃ means cutting off the hair on the breast)
This commentary refers to the passage:
“Na, bhikkhave, massu kappaapetabba.m …pe… na massu va.d.dhaapetabba.m… na golomika.m kaaraapetabba.m… na caturassaka.m kaaraapetabba.m… na parimukha.m kaaraapetabba.m… na a.d.dhaduka.m kaaraapetabba.m… na daa.thikaa .thapetabbaa… na sambaadhe loma.m sa.mharaapetabba.m".
(Bhikkhu, the beard should not be trimmed, the beard should not be enlarged, should not be cut into a ball- or cluster-shape, should not be cut into quadrangular shape, should not be cut around the _mouth_, should not be cut in 'half-dyad', should not be arranged in whiskers, the hair should not be made grown at pudendum.)
Culavagga 2.134 5.Khuddakavatthuuni
Thanissaro Bhikkhu writes in this regard:
"The beard is not to be dressed. The beard is not to grown long. It is not to be dressed as a goatee. It is not to be trimmed as a rectangle. The hair of the chest is not to be dressed. The hair of the stomach is not to be dressed. (The translation of these last two statements follows the Commentary. An alternative translation, not supported by the Commentary, reads them as prohibitions connected with facial hair, in which the first one (parimukhaṃ) could be read as "moustache" and the second (aḍḍharukaṃ or aḍḍhadukaṃ) as "a mutton-chop beard.")"
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Indeed what a phantasy it would take to dress the hair of the chest and stomach!
So evidently the interpretation of 'parimukhaṃ' as 'in front' ignores the Vibhanga, and is based on the unrelated commentary.