My only guesses, which really are only guesses are:
1. When choosing the shaping points, the software somehow confuses their order or misinterprets the difference between a Waypoint (a point that MUST be passed through) and a shaping point.
If it confuses the order, overlapping the first point of one segment of chopped route with the last point of another, then a 'ride forward, make a U-turn, ride back, make a U-turn, ride forward' may well occur. Imagine it perhaps as two pieces of string, each a foot long. Lie them exactly end to end and you'll have one piece of uninterrupted string, two foot long for you to ride along. Overlap them by an inch and the combined length will shorten by two inches. More importantly, to ride along the combined length following the strings exactly, you would need to make two U-turns. It's probably not a perfect example as in your version the total length did not reduce, or you didn't say that it did. That may mean that my string theory (ho-ho) is cock or that the software somehow makes an allowance for the overlap, tacking an additional inch on either end.... As it still gets you from and to, two very definite start and end points, which it knows it has to include.
2. Somewhere in the conversion between whatever file type Best Biking Roads uses and BaseCamp there is a slight variation in the map / road position and the 'fixed' spot of the shaping point. If the fixed spot happens to coincide with the other carriageway of say a dual carriageway, then indeed it will create an instruction to make a U-turn in order to pass you through it.
That is all supposition. I do copy third party routes and manipulate them too. That being said, I do know that the mechanics of joining two routes together differs between Mapsource (where I got quite good at it) and BaseCamp ( where I am still learning) quite significantly, or at least appears to.
Tracing over often remains the one really reliable method; that was true in Mapsource and I think BaseCamp. It's made easier if you let the software do the gruntwork first. Here's how:
Have the copied in route or track displayed.
Ask the software to create a simple route from the same start and finish points, displayed in a different colour.
Use the elastic band / shaping tool to pull the second route into line with the first.
Check for any obvious anomalies and / or fine tune out any bits that you might like to improve. This is often best done by zooming in and out. Why check?
(I) Because roads and junctions do change. There may well now be a ring road to take you around a snarled up town that was not there when the track or route you have borrowed was first created, or maybe a new one way street has appeared.
(II) Bods do make mistakes. They depart from their intended route by design (lunch calls or there is a road closure) or accident (they get lost) and then forget to correct their deviations in the final track or route they offer up to posterity. I have done it myself. If they make an error, your tracing over or converting their route into yours will repeat the same error. They also make mistakes tracing; I do for sure.
Job done.... Though I fear it may not resolve the question properly.