Well we don't know much down here but Florida code says otherwise.
Where does the code say that the dishwasher must be drained into a garbage disposal?
802.1.6 Domestic dishwashing machines
Domestic dishwashing machines shall discharge indirectly through an
air gap or
air break into a standpipe or waste receptor in accordance with Section 802.2,
OR discharge into a wye-branch fitting on the tailpiece of the kitchen sink
OR the dishwasher connection of a food waste grinder. The waste line of a domestic dishwashing machine discharging into a kitchen sink tailpiece
OR food waste grinder shall connect to a deck-mounted
air gap or the waste line shall rise and be securely fastened to the underside of the sink rim or counter.