Why Can't the passage of acquired behavior be considered acquired inheritance?
Yes, a behaviour is definitely a phenotypic trait.

Some acquired trait (typically behavioural traits but not only) can indeed be transmitted to a few future generations. But make sure to understand the mechanism. I can think of 3 different mechanisms:


epigenetics
covariance between parent fitness and offspring fitness (within one genotype and one environment) typically due to to parental care.
Transmission of tradition (in the broad sense). A tradition is also sometimes called a meme.


One will need a link to the specific paper you are reading to know what mechanism is in play in the study you are reading.