You already agreed that if you buy an item for $100 and pay a total of $130 with the tax, it is a 30% tax. The Fair Tax people claim that same $130 equals a 23% tax.
Any propaganda is coming from the Fair Tax people who want to hide the fact that they need to impose a 30% tax to equal the same amount of revenue currently raised by the income tax, payroll tax, gift, and estate tax.
If your state sales tax is 6% and you purchase a $1000 item, the sales tax is 60$ for $160 total. The Fair Tax people would claim it is a 37.5% sales tax.