Is it true that ...

Line transects must be randomly oriented?

That depends upon how you are going to use the data. In general, the answer is NO. Any orientation of lines is unbiased, and some would give superior results to a random orientation.

In timber work we are sometimes measuring the item crossed by the transect as a diameter at right angles to the centerline of the stem, rather than as an ellipse along the actual line of travel. This is a convenience to the measurer, but is always smaller than the actual cross-section which the line travels across.

In these cases, we apply a correction term of (PI /2) to increase the approximate area measured by the diameter. The validity of this correction is only insured if the lines cross the pieces at random angles. Therefore, the pieces must be randomly arranged (not usually the case, and almost never known to be the case) or the lines must cross the pieces at right angles – which is easy to insure by setting them out at random directions.

For some time now the line transects have been put out in triangles, which insures a mixture of crossing angles with oriented pieces (like blowdown) and this technique is just as easy to do with much improved results. In this case the first leg of the triangle is randomly oriented.

If however, you we not applying the correction term (PI/2) you do not need to set up the transects at random angles.