Is it true that Swissair wanted to be a global carrier? I think so. In fact, they formed the first major global alliance with Delta and Singapore Airlines, though, not a successful one.
Is it true that Swissair failed mostly due to their bad investments? I think so, too.
However, I don't necessarily agree that Swissair made those bad investments because they wanted to be a global carrier.
IMHO, Swissair made those bad investments because they felt a need to get a foothold in the EU market, as Switzerland is surrounded by the EU but is not a member of the EU. Other than SAA, all their major investments were in airlines in the EU. Without a strong presence in EU, they would likely to disappear, too, but probably later. They were in a no win situation.