The map actually just shows that you can travel via the Middlesbrough Routeing Point Group (RPG), rather than Middlesbrough specifically. The RPG includes Thornaby, Eaglescliffe and Middlesbrough; RPGs are indicated through the use of a green square rather than a green circle.
Allowing the double back here makes sense, as not all trains call at all of these stations.
When tracing a mapped route, doubling back is permitted between stations belonging to an intermediate RPG, however this only applies for "interchange purposes" - thus implying you can't break your journey at a station where you are doubling back.