As for the statement of al-Bukhaari: "It is not said that such and such is Shaheed", then Ibn Hajr said commenting on his words, "Meaning, in absolute sense"
The meaning of the words of al-Bukhaari and Ibn Hajr is that we do not rule about the one killed on the battlefield that he is Shaheed and that he will enter Paradise. This is because entry into Paradise is a matter that rests on the intention of the one killed, and that is only in the knowledge of Allah. It is also a principle of Ahlus-Sunnah wal-Jama'ah that we do not rule a person to be either in Paradise nor Hellfire.
As for calling the one killed in the battlefield a "Shaheed" in order to apply the legal rulings of a Shaheed, based on a strong speculation, hence, not wrapping him in a shroud, nor washing him, nor praying over him, then this case has been supported by the vast majority of the Salaf and the Khalaf.
Thus, Ibn Hajr states, "Due to this reason, the Salaf practiced calling martyrs of Badr and Uhud and others "Shuhadaa`", intending by it, the apparent ruling based on a strong speculation - and Allah knows best" [Fath al-Bari 6/90]
In fact, some of the Muhadditheen, such as Ibn Katheer would use the phrase "Istush-hida" (meaning "became Shaheed"
for someone who did not even die in a battle. So he says about al-Fadhl-ubn-ul-'Abbas in al-Bidaayati wan-Nihaayah [4/96]: "Istush-hida (He became Shaheed) due to a plague epidemic". Likewise, he says about al-Haarith bin Hishaam [4/95] "Istush-hida bish-Shaam" (meaning, 'he became Shaheed in Shaam')
Ibn Kathir also says about an-Nu'maan bin Muqrin al-Muzani [4/123]: "['Umar] al-Faarooq sent him is a leader over the forces to Nahaawand. So Allah bestowed by his hands a great conquest, and Allah established him in that land, and established him as an authority over those servants, and through him Allah established the Muslims there until the Yawm at-Tunaad (lit. the Day of Calling - meaning the Day of Resurrection), and He granted him victory in this world, and on the Day when the witnesses will stand forth, (i.e. Day of Resurrection). And He granted him, after seeing how he loved the magnificent Shahaadah, which is the desired objective. So he became from those, about whom Allah, the Most High said in His clear Book, which is the straight path, "Indeed, Allah has purchased from the believers, their lives and their properties, and in return, for them, is Paradise" [at-Tawbah]
Footnote:
1 In fact, Sheikh Bakr Abu Zaid - may Allah preserve him - has sufficiently dealt with this term in his book "Mu'jam al-Manaahee al-Lafdhiyah" where he says:
Al-Bukhaari - may Allah have mercy on him - said in his Saheeh: Chapter: It is not said that so and so is Shaheed. Ibn Hajr said [commenting on it]: "Meaning, in absolute sense, unless it is reported in revelation. As if [by this statement] he is referring to the Hadeeth of 'Umar".
In the book: "an-Nadhrul-Faseehu 'Inda Madhaayiqil-Andhaari Fil-Jaami'is-Saheeh" by Muhammad at-Taahir 'Aashoor, the author says on page 118 about this choice of heading by al-Bukhaari:
"This title by al-Bukhaari is strange, for indeed, to say the word 'Shaheed' for a Muslim killed in an Islamic Jihad is established in the Sharee'ah, and much frequented on the tongues of the Salaf and those after them. It has also come in the Hadeeth in al-Muwattaa' as well as the Saheehain [al-Bukhaari and Muslim], that the Shuhadaa' [Martyrs] are of 5 types, apart from the Shaheed Fee Sabeelillah [i.e. Jihad], and the description of such deeds is dependant on looking at the apparent state [of the one killed], which cannot be established by any other way. Also, in what al-Bukhaari has extracted here, there is no chain of narration, nor an annotation, which necessitates ruling out of saying: so and so is Shaheed, nor is there a prohibition for such.
Therefore, the apparent meaning intended by al-Bukhaari, is that no one should be certain about someone having achieved the reward of Shahaadah from Allah, for he does not know what this person intended by his Jihad. But this is in no way a ban, on saying about someone: He is a Shaheed, or the application of the ruling of Shuhadaa' on this person, if the conditions for that are fulfilled. Thus, the entitlement of the chapter should have been: Chapter: It is not said with certainty that so and so is Shaheed, except if based on a report from the Messenger of Allah - SallAllahu 'Alaihi wa-Sallam - such as his statement regarding 'Aamir Ibnil-Akwa': Indeed he is a striving Mujaahid.
From this perspective [it is like] the Messenger of Allah - SallAllahu 'Alaihi wa-Sallam - rebuking Ummul-'Alaa' al-xxxxxxiyah when said regarding 'Uthmaan Ibn Madh'oon: My guarantee for you, indeed Allah has honoured you. So he said to her: And how do you know that Allah has honoured him?" - End of Quote.