This is actually one of my favourite GW rules. The FAQ says:
Q: Can units from allied detachment use a webway portal to enter play from reserve? (p62)
A: No.
So if the DE contingent is an allied detachment rather than the primary then they could not use their own WWP but there would be nothing stopping models from the primary detachment from doing so!
Of course, that's just a bit of rules lawyering. In 99% of cases, the answer that 1++ gave is all you need.