This is a very interesting question and I will give you an outline of the scenario I think is most likely.
I'm using the same hypothesis to explain another common observation in single nuclei RNA-Seq: In all snRNA-Seq data I have analyzed so far I have found reads for mitochondrial genes although they are not transcribed in the nucleus. How did they get there?
When doing single nuclei RNA-Seq the cells necessarily need to be broken to isolate the nuclei. The nuclear envelope is quite stable but most other cellular membranes will be permeabilized. As a consequence, mRNA from all over the cell is liberated and can stick to the nucleus. When the nuclei are isolated, the mRNAs sticking to them will be isolated too and then will be sequenced as part of that nucleus.
In the end it does not matter if the contaminating mRNA is from mitochondria or from cells taken up via phagocytosis.
I have seen mRNA from hemoglobin sticking to cell membranes in single cell RNA-Seq after > 5 washing steps, so I think it is not unlikely to assume mRNA can stick to the nuclear envelope as well.
You could try and see if the non-phagocyte genes have a higher percentage of splicing than the phagocyte genes. Since most mRNA in the nucleus will not be spliced this would be a hint that these genes come from outside the nucleus. How well this works will depend on the technology you are using. 10X only sequences the very 3' end of the mRNAs and you are not guaranteed to have a splice site in there.