You - in your work, just helped answer your own question.
In the INPUT Admittance side of the L-filter - there are two things going on.
A series pass into a parallel pass circuit.
Both are a transformation, but due to the multiple elements they include, you can think of one filter to another - then those two series into another - which is a filter yes, but is also the 50 ohm transformation that provides the filter due to the process of taking that low-impedance input from the finals output side, into that triple L filter but as a step to step to step impedance transformation window each time.
So, the conversion process is not as efficient as what it could be, but remember too, it is a filter - to be a Bandpass filter for the 27MHz signal.
When someone tunes that slug - the output of the transistor is "tuned" as a series pass to meet the input impedance of the first element of a triple L filter.
It is best to break down the elements - these circuits - into separate transformations - then the issue of how they merge the impedance from one side - transformed - into the 50Ω you'd want for the unbalanced output is better understood - at least you would know why they used the values of capacitance they did as a means of a working window of admittance that the coil would not have enough "Q-factor" to make a difference on.
The keyword is unbalanced - so the load is a reactive (or in the realm of resistive - dummy loading) 50 ohm impedance.
