Hi Gregory,
I suspect there is a mismatch between the chromosome names in the reference genome compared to those in the annotation file used by featureCounts.
While hg19 and GRCh37 are the same genome build, UCSC appends "chr" to the beginning of the chromosome names, e.g. chr1, chr2, etc. On the other hand, Ensembl leaves the chromosomes as is: 1, 2, etc. Another difference is the mitochondrial genome, which UCSC labels chrM and Ensembl labels MT.
What are the chromosome names in the annotation file you are using with feature counts?
John