Under the hood, sketches are passed, with very little modification, to avr-gcc or avr-g++, which are standard full-featured C/C++ compilers. In fact, the same core compiler used to build linux and many other pieces of professional and commercial software.
It IS C. They/we don't stress this because it causes people who have looked at C and had problems (like you?) to get worried. Instead they risk "offending" "real programmers" who might think "I don't want to have anything to do with some fake watered down C-like language!" (before they look more carefully.) But that's OK, because the latter set is a smaller percentage of the target audience. All those people (artists, etc) who manage to make an Arduino do something fun without panicking that they have to learn a difficult and obscure programming language (C) first are a net win.