Bradbury named Google and Apple as two such companies.
Our Revenue Minister Peter Dunne this week released a more subdued statement, acknowledging "our tax laws need to evolve" but saying the issue was "a global problem requiring a global response".
Using an Irish structure, where the corporate tax rate is low, is a red herring as far as New Zealand is concerned.
Facebook could make its sales to New Zealand through a US company and New Zealand would collect no more tax.
An internet search reveals Google and Facebook have around 2500 and 400 employees in their respective European headquarters in Dublin. That's hardly the best platform from which to allege a tax dodge.
The issue is not where the company that is selling the goods and services is based but whether that company is conducting business in New Zealand through a "permanent establishment", according to New Zealand's many double tax treaties.
That can include a situation where employees in New Zealand are essentially making sales here on behalf of a foreign affiliate.
Many companies do not require people permanently on the ground in New Zealand to make sales. Online commerce is an obvious example where people and equipment involved in the sale can be based offshore.
But even foreign manufacturers of consumer goods sold at retail in New Zealand can be structured so they pay no tax here. For some, their stock is warehoused in New Zealand to fill orders for retailers, but the selling occurs offshore.
Facebook New Zealand's financial statements show the company employs few people and has few assets here.
It earns service fees from its Irish affiliate for supposedly doing marketing and related activities in New Zealand.
If a tech company used its New Zealand subsidiary to invoice the sale to the consumer, the sale would be subject to New Zealand tax. But the tax on those sales may not be impressive.
Transfer pricing rules dictate that most of a tech company's profit will end up offshore via royalty payments and for other management services performed offshore.
Payment of royalties is not profit-shifting. Just like drug companies, the royalties rightly compensate offshore affiliates for the substantial investment risk they take in creating intellectual property.
At least with royalty payments, Inland Revenue would usually collect 10 per cent of the payment in withholding tax.
How governments intend to crack down on what Bradbury claims are tech companies "free riding on the efforts of others" is not clear.
Dunne has mentioned New Zealand's participation in the OECD project Base Erosion and Profit Shifting. This examines several pressure areas, including the application of tax treaties to profits from digital goods and services.
Governments can create new tax laws to target specific transactions.
For example, specific tax rules were developed to deal with non-resident insurers writing business against New Zealand risks or non-resident shippers on outbound freight.
These regimes deem a portion of the payments made to the foreign companies to be taxable in New Zealand. But many of these foreign companies still enjoy tax exemptions through a double tax treaty.
Getting consensus among developed countries to modify long standing international tax rules as they may apply to tech companies will not be a quick nor simple process.
The real challenge for New Zealand is how to attract more of the real value-adding activities of these tech companies into New Zealand and keep more profits here.
Mark Loveday is a transfer pricing partner at Ernst & Young.