Forbes: Ted Cruz’s Business Flat Tax is a VAT
http://www.forbes.com/sites/beltway/2016/01/15/ted-cruzs-business-flat-tax-is-a-vat/#5f49e114580f
Ted Cruzs and Rand Pauls Strange Embrace of the VAT
http://www.nationalreview.com/article/426469/ted-cruz-rand-paul-vat
The Tax Foundation: Ted Cruzs Business Flat Tax is what most tax policy experts would call a tax-inclusive subtraction-method value-added tax (VAT) or a business transfer tax (BTT).
http://taxfoundation.org/blog/ted-cruz-s-business-flat-tax-primer
From the Tax Foundation article on Cruz’ plan you linked to:
“It would not be similar to existing sales taxes, or the VATs in Europe, because it would not be levied on a transaction-by-transaction basis.” Emphasis on the word, “not”.
I’ll be the first to admit I am not clear on all the various permutations of tax plans, but it does seem clear that the Trumpeters tend to dogmatically characterize the Cruz plan as being “just like” the European VAT taxes.