What are the problems with classifying IBM as a US stock for risk purposes? Is there a better way?

The problem is that IBM derives a significant portion of their revenues from abroad, so it is not a pure play on the US economy. Having said that, one could argue that since the US is a significant exporter, the inclusion of a company such as IBM in a US index makes sense.

If that is not acceptable, you’d have to include IBM in an index of international stocks.

IBM is in most North American Funds and as @bob_ stated it like many huge companies is more international than USA, but it’s registered in the states so when it all comes back home it’s a USA stock. As far as risk goes, the USA is one of the most stable markets there is and I wouldn’t envisage an inclusion of IBM stock making any portfolio excessively risky.