That's absolutely correct. There's no need to fiddle around with a mouse to write something for it to be valid. Here's what the US law on electronic signatures has to say on this topic:

In the United States, the definition of what qualifies as an electronic signature is wide and is set out in the Uniform Electronic Transactions Act ("UETA") released by the National Conference of Commissioners on Uniform State Laws (NCCUSL) in 1999.[8]. It was influenced by ABA committee white papers and the uniform law promulgated by NCCUSL. Under UETA, the term means "an electronic sound, symbol, or process, attached to or logically associated with a record and executed or adopted by a person with the intent to sign the record."

http://en.wikipedia.org/wiki/Electronic_signatures

You can type a single letter on your keyboard or just simply click a button for a contract to be signed if there was an intent to do so.