I was recently told by someone that some authentic Hadīth says reward for one prayer in al-Masjid al-Harām equals to 100,000 prayers in any other mosque and for one prayer in al-Masjid al-Nabawī (Medina) equals to 1000 prayers else where, and one prayer in al-Masjid al-Aqsā (Jerusalem) equals to 500 prayers. Whether the numbers are correct or not, and with no disrespect to these holy places, I have trouble understanding the fairness of this rule. Even if they wanted to, it is practically impossible for all Muslims in the world to live at these holy places even if these countries allow such open residence which they clearly do not. Furthermore, if miraculously everyone does end up living there, it is beyond the capacity of these mosques to hold all the Muslims. So my question is: Would it not place someone at such a disadvantage/advantage by sheer geography of where they are living or where they happen to be born? Is there any such Hadīth? Do we have knowledge of what the context of this Hadīth is?

Primarily, you have raised one question regarding the Hadīth: How can it be that Allah makes reward contingent on ‘something’ that all the Muslims would not be able to benefit from because of some limitations concerning their own selves or the holy places they are to visit? You are right. A believer should not be deprived of the reward merely because of some geographic placement. This is exactly where our religion stands. However, it does not mean that Allah should not give more importance to some places. I dare say that your question may well be raised with more vigor on the pilgrimage (Hajj) to the House of Lord. It is Allah who gives wealth to some and He, it is, who chooses for some to live in penury. Should a destitute believer be deprived of the reward that a rich person is going to earn with utmost facility and comfort because of God given riches? Would that be justified regarding as important a thing as one of the five pillars of Islam? Of course not. Thus, those who are not able to visit the House of the Lord, for some reasons, will have the same reward if they would truly cherish the wish in their hearts to visit the al-Ka‘bah. This is what exactly the case is with the three mosques. They have been given a prominent position and rank among other mosques of the world. Those who wish to pay a visit to these mosques and offer prayers therein but are deterred because of some reasons will have the same reward as those who will conveniently execute the business. Viewed in this perspective, this special rank allotted to these mosques will not be misconstrued for injustice.

Yes, there is indeed a verbatim Hadīth reported in Sunnan Bin Majah (No. 1403) as you referred to in your question. There are also many similar Āhādīth in which the Prophet (sws) has asked the believers not to travel but to the three mosques only.

Do not prepare yourself for a journey to any mosque [with the intention to earn special reward of prayers] but the three mosques al-Masjid al-Harām, al-Masjid al-Aqsā, and my mosque. (Bukhārī: No. 1115)

In another Hadīth, the Prophet (sws) is reported to have said:

One prayer in my mosque is better than one thousand prayers in any other mosque excepting al-Masjid al-Harām. (Bukhārī: No. 1116)

To my mind, it is indeed a manifestation of Allah’s mercy that His Prophet (sws) gave special reverence to these mosques so that His servants may earn a manifold reward: both who can afford a trip to these mosques and who simply cannot but they wish to.