It always refers to the subject of the sentence. If only it is correct in a given sentence, it always is better than the 'normal' possessive.
This course has introduced it too late and therefore there are many sentences which would be a lot better if they used it instead of the 'normal' possessive.
"pan" and "pani" also work perfectly well with "swój".
I think it's both: That Polish immigrants, who seem to be frequently spot in Southern England (regarding the earliest news coverage of the Brexit and how violent Brexiters started rushing for Polish immigrants) translate such sentences literally from their mother tongue, while native English people would formulate the sentence differently.