It is not whether he's natural born and therefore eligible for the presidency. It is that Ted Cruz has suggested that he did not even realize he might be a Canadian citizen until the Dallas Morning News suggested it to him and asked a few experts on Canadian citizenship law to confirm that Canada, like the US, like many, many countries, confers birthright citizenship on people born in the territory whether they request it, or want it, or not.
This is interesting because this is all happening during America's ongoing roundup of every person on the planet who may be a US citizen because they were born in the US or by birthright through their lineage, for the purpose of imposing draconian penalties for failure to file tax returns and asset information reports under the US citizenship-based tax regime. This is the only tax regime in the world that treats lineage alone as a justification to impose worldwide taxation. Ted Cruz's expressed thoughtlessness about his own dual citizenship, coupled with his breezy intention to simply get rid of the unwanted extra citizenship, beautifully illustrates the major problem with citizenship-based taxation and why no other country on the planet would try to enforce such a system.
The US is right now imposing enormous penalties and unleashing general chaos on people living in other countries with US citizenship, both by newly enforcing long-ignored rules and by layering on top of these rules a new and more draconian layer of enforcement. The chaos comes in the form of fear-inducing, devilishly complicated and duplicative paperwork, and penalties, most of all penalties, and it is being piled on to millions of people around the world, many of whom, like Cruz, are very possibly only beginning to understanding that citizenship status is mostly conferred upon rather than chosen by individuals.
Ted Cruz should consider himself very lucky, because the citizenship he claims he didn't realize he had doesn't carry any punishment for his failure to recognize it. Moreover renouncing, if he really intends to follow through on that promise, will be relatively simple, cheap, and painless other than the cost to his US political career, if any.
Not so if he had lived his life in Canada with his current apparent dual status. US citizens abroad now understand that discovering ties to the US means discovering a world of obligations and consequences flowing from citizenship that you were expected to know and obey. Ignorance of the law being no excuse, the punishments range from the merely ridiculous--many times any tax that would have ever been due--to the infuriating: life savings wiped out and many future tax savings sponsored by your home government, such as in education or health savings plans, treated as offshore trusts and therefore confiscated by the US. Moreover there is no ready escape hatch for the newly discovered and unwanted US citizenship: five years of full tax reporting compliance must be documented, appointments must be made with officials, fees must be remitted, interviews must be conducted, and in some cases exit taxes must be paid. If some in Congress get their way, renunciation could even mean life-time banishment from the US someday soon.
In the grand scheme of things Ted Cruz's citizenship is a non-story. But for what it illustrates about citizenship-based taxation, it could be the story of the century.