They're probably referring to fine-tuning on private/proprietary data that is specific to a use case. Say a history of conversation transcripts in a call center.

Larger models, like OpenAI's GPT, don't have access to this by default.

OpenAI’s API has fine tuning options for older GPT models: davinci, curie, babbage, and ada

It doesn't for the newer (relevant) ones. Fine-tuning them is expensive and slow, because they are large

Smaller models are likely more efficient to run inference and doesn't necessarily need the latest GPU. Larger language model trend to have better performance over more different type of tasks. But for a specific enterprise use case, either distilling a large model or use large model to help with training a smaller model can be quite helpful in getting things to production - where you may need cost-efficiency and lower latency.