Then you guys need to tell the "person who schedules YOU" that there is a problem.

Sorry, I know this is not FI, but got to get it straight..
The title of the tread is confusing. Almost sounds like DCI guys call themselves Delta employees.
If your company can't deadhead you right - maybe it is not Delta's fault?
If it happens a lot there must be details in you contract with Delta allowing that.
And if your company negotiated a crappy contract to cut corners with its front line employees to - probably - score more bonuses for the exacs... it is not Delta's fault either.

At Delta there is no problem with PS.