I have never heard of this and the website never seems to allow it, but I am sure if you know the managers on either side they have ways to allow it. I am 99% sure they all use the same system since at the airport return, it's the same person with the same tablet that handles returns for National, Alamo and Enterprise.
I think sometimes if you ask they may allow it if that's where they need cars in the city location.
I picked up a car at National recently at the airport, and the previous searches on the car's onboard GPS was showing someone was finding an Enterprise city branch so the cars definitely move between airport National and local city branches so the fleet is shared, but I also think they prefer to keep the fleet separate when possible. I have noticed the cars meant for Enterprise city branches don't usually have the barcode on the windshield while all the airport location cars tend to have the barcode sticker.
I do wonder though why EHI doesn't just consolidate Enterprise and National into a single brand or make all their city corporate locations co-branded between National/Enterprise if they are literally the same company and same fleet. I see Hertz co-branding with Thrifty/Dollar at all the city locations. I get it that "National" is meant too be their premium brand, but I have never had an inferior or bad experience at Enterprise and it's literally the same cars. I prefer National for the free upgrades as an Exec Member but sometimes it's not worth it since for National I have to rent at an airport and pay the 20% "premium location surcharge" while for Enterprise it's next door.