In Linux Mint 17, I can confirm the existance of both /usr/bin/mintbackup and /usr/bin/mintBackup
I cannot reproduce the OP's problem.
Furthermore, it doesn't make sense that mintBackup (with capital) would do anything different because the contents of mintBackup is
#!/bin/bash mintbackup
and doesn't forward any arguments to /usr/bin/mintbackup.
In Linux Mint 17, I can confirm the existance of both
/usr/bin/mintbackup and /usr/bin/mintBackup
I cannot reproduce the OP's problem.
Furthermore, it doesn't make sense that mintBackup (with capital) would do anything different because the contents of mintBackup is
#!/bin/bash
mintbackup
and doesn't forward any arguments to /usr/bin/ mintbackup.