I agree AMT itself is not a particularly complicated calculation. But I don't think that was really the point of that quoted statement. The complicated part is figuring out if and when AMT applies to you, and, essentially, for how long it can raise your taxes.

As you said, the tax code requires you to calculate your taxes twice - once using the "normal" rules, and another time using the AMT rules, and you pay whichever is higher. So, depending on your individual circumstances, it's non-trivial to know if AMT will apply to you when making particular money movements during the year. Also, if you have to pay AMT in year one, but then in year two the calculated AMT is below your normal tax calculation, you get a credit for the excess amount (i.e. amount over the normal tax from year 1) up to the delta between the normal tax and the AMT amount. In other words, AMT can often times just cause tax to be paid earlier, but the total amount of money (over years), ends up being the same. Of course, the time value of money comes into play - paying a tax earlier is losing money.

So, point being, there are complicated considerations to take into account.