There is halakhic justification for the custom of vocalizing a stress-less feri as a more grammatically correct way of saying the blessing. In his responsa Or Letzion, (vol. 2, chapter 46, halakha 34), the Sephardic rabbi, Ben Tzion Abba Shaul (1924-1998), wrote:
יותר מדוקדק לומר בורא פרי הגפן וכן בורא פרי העץ ובורא פרי האדמה
כשהאות פ' של המילה פרי רפויה
שכן אותיות בג״ד כפ״ת אחר אותיות אהו״י רפויות הן. ואין לומר שיש הפסק בורא לפרי, שהרי המילה בורא אין לה משמעות בפני עצמה, ועל כרחך שהמילה פרי נמשכת אחר המילה בורא, ואם היה זה פסוק בתורה, הטעמים היו מאריך טרחא סוף פסוק
It is more accurate to say borei feri hagefen and also borei feri ha-etz and borei feri ha-adamah with the letter peh of the word as a stress-less feri.
This is because, grammatically, the letters bet, gimmel, dalet, kaf, peh, and tav, when following the
letters alef heh vav and yud become stress-less. And it is not right
to say that there is a pause between borei and peri, since
the word borei [the Creator of] doesn't have a meaning by itself,
as it is necessary for the word feri [fruit] to continue after the
word borei to make sense. And if it was a verse in the Torah, the cantillation
would be a ma'arikh tarḥa sof pasuq.
It should be stated that the custom for many Sepharadim is to still say peri with a stressed peh. R. Ovadia (Yabia Omer, O.Ḥ. 9:22) specifically countered the position of Or Letzion, stating that, grammatically, there should be a stressed peh because there actually is a brief pause between the two words in the blessing. The grammatical rule applies to words joined by context. Among other proofs that he uses from Tanakh, he cites a very similar parallel in the vocalization of Gen. 1:11, where a peh follows a heh (which should normally make it stress-less):
עֹשֶׂה פְּרִי לְמִינוֹ
'oseh peri le-mino
Moreover, R. Ovadia goes on to say that the grammatical rule above is not so firm:
ובכלל נראה שהכלל של אהו"י הסמוכות לבג"ד כפ"ת שעושות אותן רפויות, אינו
כלל החלטי, ופעמים רבות שדוחים כלל זה מפני סיבות אחרות מוצדקות
In any case, it doesn't seem like the rule of the letters alef heh vav and yud in connection with the bet gimmel dalet kaf peh and tav to make the latter stress-less --is actually a decisive rule, as there are plenty of times when that rule is rejected for other justifiable reasons.
R. Ovadia then proceeds to list various other occurrences when the rule is not followed (e.g., mi khamokhah ba-'elim Hashem, mi kamokha ne'edar ba-qodesh) to dismantle the stringency of the grammatical rule.