I thought it was common for hotel to allocate some rooms for the OTA and other travel channel partners.
When their own non allocated inventory runs out, they cant just sell those pre allocated ones.

I experience similar case in Singapore.
At Park Royal on Pickering Hotel. I need to extend the stay for 3 nights and the FD told me that its better for me to book through OTA if I can find cheaper rate as their own inventory is low and they need to charge me higher rate for the extension.
End up booking the extended stay with OTA with similar room type and we keep the room throughout.