It's difficult to say without more context, but it probably means they did not have the facts to support their argument. http://idioms.thefreedictionary.com/not+have+a+leg+to+stand+on

This sentence is vague, I can’t tell if it’s litteral or metaphorical. Assuming we’re really talking about “legs” the sentence should be broken down like this: “I got to see, first hand...” meaning “I was able to verify for myself...” “...just how little legs we had to stand on,” meaning “...the small number of legs we had to support ourselves.” I hope this helps!

The expression has used an incorrect word. "little" should be "few". "You have few legs to stand on" or "You don't have a leg to sand on" indicates you can not support what you are saying or doing.