We wouldn't use this argument ourselves, we really wouldn't

The intention behind the argument is just fine - let's not be protectionist over who owns companies. But we have to admit that we're not very much taken with the argument itself:

Those bloody foreigners, they come over here nicking our companies. For critics of foreign takeovers, 2016 has been the stuff of nightmares.

First brewing giant SAB Miller was snapped up by an overseas rival, and now the London stock exchange and chip-maker Arm look destined for foreign hands, much to the fury of those who believe such a fate tends to be negative for businesses and the economy.

Critics like to pretend that overseas buyers pillage Britain’s best silverware, gobbling up prized technology and scientific and industrial know-how, while shutting down factories, firing workers and eventually scampering back to their homeland with the best bits of British plc.

It doesn’t take a genius to realise that such bashing doesn’t stand up to scrutiny.

ARM was majority foreign owned before Softbank appeared. From memory some 43% US and 15% European share ownership, although this is complicated by not knowing who owns the funds that own the shares. By whatever standard we might use about foreign ownership it was thus already a foreign company.

SAB Miller is a rather different case. That's a company that was listed in London, yes, but it's not obvious that the company has anything other than the most passing interest in the British economy. The major subsidiaries are:

Bavaria Brewery
Foster's Group
Kompania Piwowarska
Miller Brewing Company
South African Breweries
Pilsner Urquell Brewery

A more detailed look at regions of operation show nothing at all in the UK. And no, UK Fosters is brewed, we're told, by someone else under licence. 

The argument we would have used is that you can't go around complaining about foreigners buying a British company which owns lots of foreign companies. For your current complaint is that the British company should never have bought those foreign ones in the first place. At which point protectionism about ownership dissolves in its own contradictions.