"Well", "Um/Hmm...", "Let's see..." that you mentioned is the most common use of 글쎄(요). The way it is said can vary though. It is often said with hesitation but not always. Sometimes it is said clearly just like any other words.
There is also a second use of the word, which is like an opening word when reiterating one's point, like "but I'm saying ..." (in an argument or heated discussion). This might look in conflict with the more common usage, but not necessarily so, since it's like a dismissive "whatever" on what the other person said. In this usage you typically say it more firmly with emphasis. E.g. 글쎄 내가 안 그랬다니까요 (I'm telling you again I didn't do it).
I don't know exactly how that person said it, so, but as I said, it can be said firmly unlike an equivocating "Well, ..." or something similar.