That's too much effort. Should have been a browser extension that uses ollama so it can run with local models or maybe even openrouter...
But, there is a reason why it's not an extension. At least for now. Whole product isn't a UI or service, it's a set of skills for your AI agent of choice, which gets content from URL or whatever shared as a source, splits it into claims and does extensive web searches for every claim to compare it with statement from provided content.
On local models constraint isn't a model itself - but search. Model don't judge from it's trained memory, so even local model will need a backend for search, otherwise it can't provide a verdict.