According to samtools:

Important note: when multiple regions are given, some alignments may be output multiple times if they overlap more than one of the specified regions. However, if I have such a bed file:

chr1 3033215 3044215 ENSMUSG00000090025.1/Gm16088 0 +
chr1    3033216    3044416    ENSMUSG00000064842.1/U6    0    -

Samtools counts the read only once:

samtools view -c -q 1 -F 4 -L matrix_small_f.bed super_short.bam
1
samtools view -c -q 1 -F 4 -L matrix_small_f.bed super_short.bam
HWI-ST227:372:C3UVCACXX:3:1212:16462:69280    0    chr1    3044215    255    50M    *    0    0    TCCAAGATTGGTGCCGAGCCCTATTGGCCCAAGTTAGAAGTAGACATCTG    CCCFFFFFHHHHHJJJJJIJJJJJIGGJJJJJJHHIIJHIBFHIJJJIIG    XA:i:0    MD:Z:50    NM:i:0

If I split my bed file into two separate files containing the first and the second regions, samtools shows the same read for each file.