Richard:

You're right, holidays might help to bring # of days below 91, if Shimla did not arrange to have his mondays off counted as vacation time.

There's still another potential problem. The IRS changed recently their rules to count every day of presence in the US, including days of arrival and departure. That burned a lot of canadians. IR could also change their rules at any time and that's something to have in mind.

IR will not usually audit every commuter who does not file a tax return, but they sure can. It has happened and it is perfectly legal. They recently sent a tax bill to a British citizen who claimed non-domiciled status and stayed in the UK for just 30 days in a year. They do monitor your stays in the UK. Yes, it's not their business but they're the government and they can do whatever they want. And it gets worse by the minute.

It's easy for a foreign executive not to be taxed in the UK thanks to the non-domiciled loophole. For a british citizen the only way to not owing a single penny to IR is acquiring non-domiciled status and that requires almost no visits to the UK.

IR will know if you're filing taxes in Switzerland if you're an UK national. They have a tax treaty remember? Tax treaties imply exchange of information. If you're british, every tax return you file in Switzerland will be sent to IR.