While RCB is clearly being an idiot here, let me point out that Cauldron as a whole hasn't done much by way of poking their nose into things yet.
Most likely because any reasonable person would realize having DARPA develop and manufacture tools that can help against Endbringers and Scion advances their goals without draining their resources. After all, to Cauldron an army division that uses new tech to take out an Endbringer but is wiped out in the process represents hundreds of saved Parahumans, and any useful human assistance against Scion improves their odds in the end.
Since it can be argued Cauldron lacks reasonable people, let's instead say they are willing to reap the benefits of DARPA's investment, and not risk slowing down their development cycle. No reason NOT to let the people charged with military R&D do the R&D you ultimately want done and will benefit from if you let them do it.
Besides, the only thing about Brockton Bay that matters to Cauldron is their experiment, and "Non-parahuman agency manages to regain control" is a valid if unexpected result. Most likely, they will choose to replicate the experiment elsewhere, and continue to monitor events in the Bay Area going forward for further insight.
In short, we have one proven idiot so far. We don't have proof that she has support from above, only that she is abusing her authority over those below her...