Arduino with assembly?

The Arduino boards can be programmed in assembly. All you need is an ICSP Cable (In Circuit Serial Programmer) and the AVR toolchain (free from ATMEL) to write to the board. You then get the advantage of on board debugging.

As you suggested, you can just slap an ATMEL chip on a breadboard and go to town.

The kit you referenced looks like a great starting point. You can take the chip right off the board and stick it on your own breadboard (as long as it has correctly regulated power and you account for the clock).

EDIT: Apparently you don't need an ICSP to load assembly programs. See comment below for details.

The Arduino IDE can be "fixed" to accommodate Assembly code. Here is the wiki: http://www.cs.nmsu.edu/~jcook/arduino/index.php?n=Notes.AssemblyMods

As far as I know there should be nothing specific about the Arduino bootloader that could prevent you from using assembly instead of C. The Arduino IDE may make it difficult to upload you own .hex files but it looks like the Arduino bootloader is STK500 compatible so you should be able to use it with avrdude.