What is being described here is called "offloading" in the Philippines. I know several Filipina women who had legitimate trips ruined over it. It is theoretically the benevolent government's all out effort to protect it's population from the perils of human trafficking. The theory being that the innocent naive young Filipina is being lured to Stockholm by the OP to be sold into slavery or something and she must be barred from leaving the country for her own protection. But the policy is implemented by officials who are legendary for their corruption and it rife with stories of extortion, bribes, payoffs by REAL traffickers and everything else. CRK is notorious for being one of the most corrupt airports in this regard. CEB probably comes in second. MNL is allegedly less corrupt and would be a better departure choice since theres a problem though it happens there as well. However, since there is a problem, the OP might do well to just go there and travel back with her, from MNL. They are much less likely to try such shenanigans when the foreigner boyfriend is present.
The $2000 would be what is called “show money” in the Philippines. The theory being that if you can afford to travel you ought to be able to demonstrate it. It is not an unheard of request in the Philippines. Unfortunately having a big stack of cash in a situation where extortion is not unheard of is not a good place to be.
Of course while the scenario described is very real, it does also make great material for scams too so be wary. But that no cash has changed hands (or refundable airline tickets “disapearing”) makes the story more believable. I love the Philippines and the Filipino People but it can be a really messed up place sometimes.