It's not a coincidence, but also it is.
Here's why it is not. The meaning of the Hubble constant is that just as you need approx. 14 billion years to cover one megaparsec at approx. 70 km/s, you also need that much time to cover a proportionally larger distance at a proportionally larger speed. If you set the speed to c, you end up with c*14 By = 14 Bly.
That is to say, if everything were always receding at the velocities given today by the Hubble's law, it'd take the reciprocal of today's Hubble constant for all distances in the universe to shrink to zero.
But the recession velocities were not constant throughout the history of the universe. If, for example, we'd have the recession velocities be higher in the past, then the actual age of the universe would be lower than what we get from the Hubble's law today (i.e. you don't need 14 By to cover 1 Mpc if for half the journey you traveled at e.g. 140 km/s and slowed down to 70 km/s only later). If, on the other hand, the recession velocities were lower in the past, then the age of the universe thus calculated would be higher.
Here's where the coincidence comes in: it's a coincidence that we live at a time in the history of the universe when the periods of deceleration and acceleration took about the same amount of time, with about the same but opposite nett effect, and the resultant expansion curve happens to be - to an o.k. ballpark - approximated by a line.
Yet, it is only a ballpark figure. Today, what you get from the detailed model differs by a good few hundred million years from this approximation. Some aliens living some couple billion years in the future will find the approximation exactly right (and they'll think it a massive coincidence, I'm sure).
But all the aliens living afterwards will find this approximation ever more inaccurate, as the Hubble parameter asymptotically approaches a constant value - and so, does too its reciprocal - while the time on the universe's clocks keeps ticking for all eternity. The two values will keep diverging.
An alien 10 billion years from now will find the reciprocal of their Hubble constant show approx 17 billion years. Another one living 100 billion years later will calculate almost the same value. Nobody will ponder a coincidence then.