The phrase "open source" is applied loosely in this space and is stricter than "open weights" in its usual software sense. When a page says open source about a model, treat it as "the weights are available," and check the rest for yourself.
Running open weights also means taking on the operations: hardware, a runtime, upgrades, and someone who notices when the process dies. That cost is the honest trade against a hosted API. See open source and proprietary models.