I think that reasoning is very strained myself.

It's ungrammatical to use it in the sense you claim it is intended. And since it is commonly misunderstood in the sense of exertion rather than the action of using a strainer, whether successfully or not, that suggests that the average English reader either then or later did not recognize it as a familiar expression meaning what you say it means, which, if they did, might justify its grammatical oddness.

As I understand it the Greek says "out" but I'll say no more.