You are right!!!
The word "Reiver" means a plunderer or raider. It comes from the same origin as the word bereave.
At the time of Shakespeare in the 1500's, while all was quite peaceful elsewhere in Scotland and England, the Borders area was dominated by clan families, such as Armstrongs, Douglases, Scotts, Johnstones, Elliots, and many others.
Crossing the Border into England and stealing cattle and livestock was a favourite pastime, and much blood was shed as a consequence.
This is one of the reasons why there are so many Castles and fortified houses called Peel Towers in the South of Scotland.