Without going into much detail, permanent establishment generally defines when a business is treated as operating in a country. The specific conditions are set forth in various tax treaties between the US and other countries. Generally, having an employee residing in the US and working for the business (whether or not as owner) is usually treated as resulting in a US permanent establishment, meaning the business is treated as operating in the US. If you are from a country which does not have a tax treaty with the US, the issue is generally much simpler: does the business have any income-generating operations in the US?
The second consideration is sourcing of income. IRC 861 and 862 define what income is US-sourced and what income is foreign-sourced. Generally, income from US customers or US payors is US-sourced income, and the same income from foreigners is foreign-sourced. For income taxation purposes, this distinction doesn't matter but it does matter for non-tax purposes. The H1B restricts the employee from engaging in US employment or business activities, but does not restrict their non-US employment or business activities.
A blog hosted on a foreign host, targeting a foreign audience, and earning foreign ad dollars is not a US business and generally should not violate the H1B rules, however you need to talk to an immigration attorney to make sure the analysis applies to the specific blogging activities you would be engaging it.
What you can't have on H-1B is the wage from 'unapproved' sources. You will need to get H-1B for every wage source. But there is no restriction on you receiving dividends, capital gains, etc.
Don't confuse "revenue" with income and "wage" with income. Income can be wage, dividend, capital gains, etc. H-1B only restricts 'wage'.
You could just ignore this, like I do, but if you're in America on an H1B visa, which I'm not, then you're probably best off following the rules, lest they expel you and never let you back in, without giving you time to organise getting all your stuff back first.
Do you have any links that show that ads on a blog are legal? All the research that I've done came to the same conclusion.
We should not have to come up with "creative ways" to do something simple like ads on side projects (be it a blog or a free app).
I would not risk my status here or the possibility of owning a green card for a side project that makes me a couple hundred dollars a month. It is not worth it.
It is ilegal to even make money on ads on a blog... this completely sucks and is very frustrating.