We have tried SRTM v 4.1 DEM as well as ASTER GDEM2 for the same purpose, and in both cases, we experience the problem mainly in floodplains (in low elevation areas) as well as in large reservoirs (in the high elevation areas of the Western Ghats). We have gone through several literature on this regard and we need to sort this issue out using Python based scripts.
In order to ovoid pseudo-parallel-drainage lines in flat area have you try to burn you DEM with GIS hydrological data (stream burning : Hutchinson 1989; Maidment 1996; Seyler et al, 1999; ....)
OK. Stream burning is a good option if we have the actual stream network data. But I'm working for a pretty large region and I don't have the stream network data.
I came across this type of situation when processed area is very small. you can get rid of this situation by increasing the threshold value if you are processing very large area,
Another option of getting the stream network is to digitise from public web GIS like google earth, but be careful about model and spatial reference.
The problem is not with the outlook, but it is all about the number of streams generated. In such flat areas, several parallel, first order, streams will be generated during the process. In the case of basin morphometric analysis, the number of first order streams will be too high and it will affect the accuracy of morphometric parameters. That's why I specifically asked to remove the parallel pseudo drainage lines.