One trick used to push profits offshore is to use "transfer pricing": transactions are made with a subsidiary based in a tax haven (either part of the same legal entity, or a partner/shell company used to the same effect), with prices skewed so that the offshore company comes out with a huge profit. (Googling around, I found http://repository.essex.ac.uk/8098/ which seems to my untrained eye to give a reasonable overview of this).

For example, the subsidiary company might have ownership of a trademark, and the onshore company pays a ludicrous amount to license that trademark. The accounts show this as a cost for the onshore company, lowering its profits; whilst the offshore company makes a large profit. An example I've come across (but can't find/verify them at the moment) is pencils being bought from an oversea office for thousands of dollars each.

If corporations were charged based on location of costs rather than profits, as you suggest, I can imagine this being used the other way: almost all of a company's assets, from across the globe, are funnelled into an offshore division, in order to pay a ludicrous amount for some trivial local item (e.g. rent and security guard for their empty 1-room office).

PS: I think these sorts of tricks are the reason the article keeps using the phrase "tangible assets", rather than just "assets".