It depends how you pronounce it. To say "it doesn't matter" you say it fast, as if it's one word. If you mean "It is equally much" you make sure to pause between the words.
Also, the last phrase is usually used to talk about measurements, like "there is equally as much sugar in this cup as in that one", so telling one meaning from the other is very easy once you look at the context.
It depends on how you pronounce it. I live in Copenhagen too and I see what she means. If you say it fast, like you usually do, the phrase means "It doesn't matter". But if you slow it down and make sure to pause between the words, "lige meget" can mean "equally much" or "the same amount". It just isn't used that way very often, as it usually refers to comparing the amount in one receptacte to another. And in that case the phrase would be "Der er lige meget i..."