It is difficult to know how accurate the writer is being in their terminology. In precise mathematical terms, the reciprocal of something is one divided by that thing. The "something" can be almost anything. For example, the reciprocal of 4, is ¼ (a quarter), and the inverse is also true: The reciprocal of ¼ is 4.

You can use reciprocal with physical terms and measurements. For example, period (the length of time between repetitions) is the reciprocal of frequency (the number of repetitions per period of time). A light that flashes every 3 seconds has a period of 3 seconds and a frequency of 20 a minute. Both terms ("a period of 3 seconds" and "a frequency of 20 a minute") mean exactly the same thing.

However, in less technical uses, "reciprocal" is sometimes used to mean "opposite", and sometimes writers get confused. Reciprocity is a particular form of being opposite. Whether it fits or not in your example, I cannot say.