if you purchased your computer direct from Dell and they shipped you the wrong one then they MIGHT exchange it. If you purchased it from a third party vendor then you might be out of luck.
I say might because a company has the right to make substitutions on items of equal or greater value. There is also the possibility that the website was a typo which also the company is not liable for.
I deal with Dell customer service reps on a daily basis and find them to be courteous. Like everything you have your good eggs and bad ones. If it perturbed you that much then call back and speak to a supervisor. If the only issue with the computer is lack of touch screen but everything else is up to par then I say live with it.
I bought an Insprion One 19 from Dell Hong Kong website. The advertisement shows that Insprion One 19 is a touch screen computer. However, I received an NON touch screen Insprion One 19 today.
I immediately reported my case to Dell customer service centre. They replied rudely saying