The hadith that you quoted is referenced in Sahih Al-Bukhari 8/53, among other authentic sources with the same content or meaning. The hadith is an indication that 'Umar ibn Al-Khattab was succesful in reaching these conclusions not through a direct revelation from Allah, but through strong knowledge of the religion and its principles.
For your specific request about Ibn Hajar Al-Asqalani, in his book Fat'h Al-Bari (Arabic: فتح الباري شرح صحيح البخاري), his interpretation of this hadith detailed the incidents of agreement mentioned therein, but did not address your specific question (i.e., the potential of 'Umar receiving divine revelations). Other books have done so, however.
Qadi Ayyad (Arabic: القاضي عياض) in his book Ikmal Al-Mo'allim (Arabic: إكمال المعلم بفوائد مسلم), Vol. 7, pp. 403-404 (footnotes) said:
هذه الأمور مما كان رآها عمر برأيه واستحسنها بداية بحسن نظره، ووافق ذلك من وحى الله فيها بعد، وشروعه فيها ومذهبه، وكل هذا مطابق للحديث
— NOTE: My own translation, so treat with care:
These matters meniotned by 'Umar are his opinion, which he formed in the beginning based on his good perception, and later the revelation from Allah agreed with his ['Umar's] perceptions, and this is when it became a doctrine, and all this conforms with the hadith.
Similarly, 'Awn Al-Din ibn Hubayra (Arabic: أبو المظفر يحيى بن محمد بن هبيرة) in his book Al-Ifsah 'An Ma'ani Al-Sihah (Arabic: الإفصاح عن معاني الصحاح), Vol. 1, pp. 134, said:
في هذا الحديث من الفقه أن عمر رضي الله عنه كان جدًا كله ليس بذي هزل؛ فلذلك أجرى الله على لسانه من الحق الذي لا ينزل القرآن إلا به، وكل ذلك ليس له في شيء منه هوى بل توخى الأصوب فالأصوب، والأحوط فالأحوط والأحسن فالأحسن
— NOTE: My own translation, so treat with care:
In this hadeeth from the fiqh is that 'Umar's knowledge was very well rounded, not to be taken lightly. This is why Allah has passed the truth through 'Umar's words, and it was revealed as Qur'an, which nothing but the truth comes out of it. All this has nothing with his ['Umar's] desires; rather it is be seeking the most correct, the most cautious, and the most meaningful [by 'Umar].
Abu Sulaiman Al-Khattabi (Arabic: أبو سليمان حمد بن محمد الخطابي) in his book A'alam Al-Hadith (Arabic: أعلام الحديث), Vol. 1, pp. 384, Q. 115/402 said that most likely this was a deduction on the part of 'Umar (specifically about the station of Ibrahim).
Muhammad ibn Isma'el Al-San'ani (Arabic: محمد بن إسماعيل الصنعاني) in his book Al-Tahbeer Li Eidah Ma'ani Al-Tafsir (Arabic: التحبير لإيضاح معاني التيسير), Vol. 1, pp. 412, said that 'Ali ibn Abu Talib said that he never doubted that serenity came through 'Umar's words. Al-San'ani further explains this by giving other examples where 'Umar had opinions that were later revealed as doctrine by Allah in the Qur'an, and he mentions the prisoners of war in the battle of Badr, the prohibition of Alcohol, and other incidents.
Finally, receiving revelations from Allah is not necessarily restricted to prophets or messangers, whereas receving revelations from Allah that form a doctrine is restricted to messangers. This is not to say that 'Umar ibn Al-Khattab received revelations from Allah, as we have no proof from Allah or the Prophet (ﷺ) to that effect, nor even a claim from 'Umar himself, or any other companion.
Having said that, we know that Maryam received revelations from Allah and talked to angels:
فَاتَّخَذَتْ مِنْ دُونِهِمْ حِجَابًا فَأَرْسَلْنَا إِلَيْهَا رُوحَنَا فَتَمَثَّلَ لَهَا بَشَرًا سَوِيًّا قَالَتْ إِنِّي أَعُوذُ بِالرَّحْمَنِ مِنْكَ إِنْ كُنْتَ تَقِيًّا قَالَ إِنَّمَا أَنَا رَسُولُ رَبِّكِ لِأَهَبَ لَكِ غُلَامًا زَكِيًّا
And mention, [O Muhammad], in the Book [the story of] Mary, when she withdrew from her family to a place toward the east. And she took, in seclusion from them, a screen. Then We sent to her Our Angel, and he represented himself to her as a well-proportioned man. She said, "Indeed, I seek refuge in the Most Merciful from you, [so leave me], if you should be fearing of Allah ."
— Qur'an 19:16-18
Similarly, the mother of Moussa (ﷺ) received divine revelations (see Qur'an 20:38-39), and so did the sons of Ya'qoub (see Qur'an 4:163), while they were not prophets nor messangers.