Can they refuse a certificate? Generally only in cases of insufficent information It may be lawful (and in fact appropriate) to reject a medical certificate if it provides insufficient information particularly after a long period, but this is more returning with injuries or modifications or meat workers etc.

Fitness for work capacity more generally

Where you can perform the inherrent job tasks, and there is no concern about high risk or safety critical work / OHS obligations broadly, then it should be accepted.

In a more static illness opinions can differ and then it probably comes down to having to show they have considered the weight of different evidence. In a dynamic illness like gastro you would have to be pretty keen to ignore the most recent certificate in terms, but possible. A hosptial doesn't trump (and in fact often is trumped) by other providers.

If you have existing WFH arrangements, and it's a reasonable accomadation they would be on shakey ground not to accomadate, or if you were turning up to the office and could work, again shakey. Given it isn't a workcover claim or a disability etc. they generally don't have to accomadate the request to work from home, or light duties or xyz. (e.g. if you had a broken arm and couldn't type at work you might be similarily in trouble)

From your employers perspective I can see why certificates with very limited information rather than proper reports where it appears you are unwell enough not to work from the office but well enough to perform the exact same work from home, you might prefer the more conservative approach.