That was most likely some bogus research paper written by people who did not understand what they were computing.

Even among professional physicists, a surprisingly large number of them do not have clear ideas about the meanings of the fundamental constants and of the fundamental units of measurement. The reason is that the subject of metrology, even if it is the fundament of physics, is almost never treated correctly in physics textbooks, if it is mentioned at all.

Ignoring the extra constants that might be needed in the theory of nuclear strong and weak forces, and also the extra constants that may be needed in certain variants of Einstein's theory of gravitation (e.g. "the cosmological constant"), in the physics that is encountered by the majority of people there are only 2 fundamental constants, which determine the strength of the electromagnetic interaction and the strength of the gravitational interaction, i.e. the constant of Coulomb's law of electric attraction and the Newtonian constant of gravitation.

None of these 2 constants can be claimed to be particularly close to 1, even when expressed in natural units, much less when arbitrary units are used. These 2 constants can be expressed in several equivalent ways, but none of the different values obtained thus has any unexpected values.

For example, a constant that is equivalent with Coulomb's constant is the so-called "fine structure constant" a.k.a. Sommerfeld's constant, about which a huge number of aberrant research papers have been written by people who did not know what it means. The "fine structure constant" is the speed of a particle with unit charge that revolves around a fixed particle with unit charge, when having unit angular momentum (in natural units). That speed is determined by the equality between the electric attraction force and the inertial centrifugal force, so it is a measure for the strength of the electric force and it is inversely proportional with the constant from Coulomb's law.

The poor handling of metrology in modern physics textbooks is in contrast with classic masterpieces, like Maxwell's "A Treatise on Electricity and Magnetism", which started with a good description of how physical quantities are measured and how systems of fundamental units of measurement are chosen, because without such a solid base all the following theory can be flawed, as it frequently happens in some modern theoretical research papers, where bogus numbers are computed.

In the SI system of units, besides the 2 constants of Newton and Coulomb there are a few other "fundamental constants", which are fake fundamental constants, because they are some exact numbers, chosen by convention instead of being measured experimentally, which are chosen is such a way so that the legal units, like meter, second, kilogram, have values approximately equal with the values corresponding to their old historical definitions.