What is correct syntax to swap column values for selected rows in a pandas data frame using just one line?

One way you could avoid alignment on column names would be to drop down to the underlying array via .values:

In [33]: df
Out[33]: 
       L      R  VALUE
0   left  right     -1
1  right   left      1
2   left  right     -1
3  right   left      1
4   left  right     -1
5  right   left      1

In [34]: df.loc[idx,['L','R']] = df.loc[idx,['R','L']].values

In [35]: df
Out[35]: 
      L      R  VALUE
0  left  right     -1
1  left  right      1
2  left  right     -1
3  left  right      1
4  left  right     -1
5  left  right      1