Yes, it is. Any time the word "reasonable" is part of a standard, there is inherently some level of subjectivity. Two jurors can hear the same exact testimony and one could believe there is reasonable doubt, while the other does not.
In this case, assuming the suspect didn't confess, it sounds like mostly one man's word against another. Assuming the suspect denies carrying or showing the gun, it will come down to the credibility of the witnesses. I would imagine, a key point would be whether the complainant can accurately describe the gun he allegedly saw. Even if the suspect owns a gun that more or less matches the complainant's description, that might not be enough proof, especially if the suspect legally owns a large number of handguns of different types, or if the gun is a very common type.
Unless there is video evidence, another witness, or self incrimination by the suspect, this case seems like it would be difficult to prove, beyond a reasonable doubt.