Your quote implies that the transmitter/receiver should be separated from the proto board by long wires- that's where it is telling you to put the transmitter/receivers and antenna- away from the vero board, it doesn't matter where exactly- I think that the inductance introduced by the wires is supposed to counteract the parasitic capacitances on the veroboard.
Radio circuits by their nature work with specific frequencies and parasitic inductances and capacitances (like those caused by all the generic traces on the proto-board cause problems. Imagine an R-C filter. Good right? Now imagine that instead of just plain old perfect ideal wires connecting the R and C, the wires connecting them are REAL wires. Real, really messy wires that loop all over the place and branch off and meet each other again (like all the unused traces on the vero-board). The lines that are wires in your circuit schematic aren't lines anymore, they are other capacitors and inductors. They essentially introduce extra capacitors and inductors and resistors into your circuit which will cause it to work differently. When your circuit is a radio circuit and has to be tuned precisely to work, these extra parasitic components cause problems. In the case of the R-C filter they will change the frequency that your filter will work at.