I agree, “engaging with content” is always active because otherwise language wouldn´t be processed at all. In the case of speech, if language isn´t processed it becomes either sound patterns (within in a language) or pure noise.
However, thanks to the discussion with @t_harangi I´ve come to the conclusion that the
distinction “active - passive” is better avoided in this context because it tends to create a conceptual mess by mixing three different meanings:
- Meaning 1: Listening (and reading) as “passive” in the sense of receiving input in the context of the “input - output” or “sender - receiver” model. “Active” then means outputting something (i.e., sending information), e.g., by speaking or writing. However, there are two main problems here:
- Listening and reading are always ongoing operations (activities) otherwise nothing happens. So, strictu sensu, there´s no passivity here, because operations occur or they don´t occur.
This problem can be overcome when theories, for example in sociology, switch to (communicative) attributions or paradoxa, but that´s a story for another day.
- Not all listening and reading activities are created equal, as there are different levels of depth of engagement (see our discussion above)
- Meaning 2: Passive listening as “divided attention” == the (permanent) switching of the attention focus in multitasking activities.
There´s a lot of research reg. “focused, divided, selective, etc. attention”, and the common wisdom is that multitasking is often detrimental compared to single-tasking because the quality / speed of performance decreases while the error rates increase, etc. (see our discussion above).
Talking about “passive listening” here doesn´t make sense because there´s nothing “passive” in the permanent switching of one´s focused attention between tasks.
- Meaning 3: Passive listening refers to “listening alone without other concurrent or subsequent activities” For example: Reading while listening, taking notes while listening, shadowing, writing a listening diary/summary afterwards, talking about the topics one has listened to with one´s tutor afterwards, etc.
For the sake of accuracy, it´s better to speak of “listening alone or listening as a sole / exclusive activity” rather than calling it “passive” listening.
The key question here is: What are the levels of depth of engagement for listening without / with concurrent or subsequent activities?
“a blogpost that’s making a bad faith semantic argument.” (t_harangi).
I wouldn´t called it “bad faith” in Andrew´s case. Andrew (like Benny and many others) just operated within the conceptual mess created by the highly ambivalent use of the “active - passive” distinction. That´s all.
“Does anyone know of any carefully controlled studies to test these hypotheses.”
Meaning 1 has been discussed since the time of the German philosopher Hegel. And there have been hundreds of thousands pages written about the corresponding “distinction-based” approaches, esp. since the late 1960s. However, that´s probably not interesting here unless you want to deconstruct the whole input / output and sender / receiver model of communication 
Reg. meaning 2, there is a lot of psychological, neuroscientific, etc. research out there (keywords: “divided attention”, “selective attention”, “multitasking”, etc.). Just use “Google Scholar” to look for studies (in the narrower context of SLA) that interest you.
In the case of meaning 3, “Google Scholar” is also your best friend.
Unfortunately, I don’t have time to review the literature on SLA further at the moment.
But if you tell me which topics/hypotheses are of interest to you, I will see what I can do as soon as my time budget allows it.
Hope that helps
Peter