Trying to invert the color of a Tiff and only getting outlines

Hi there,

I was given a fairly simple tiff logo file. It's black with a transparent background. I'd like it to be white with a transparent background. I'm not really sure how to do this. Let me also preface that I have Illustrator and Photoshop CS6.

I tried inverting the colors in Photoshop and the black became kind of grey, but not white. I was also given a white jpeg version of the file, but both the image and the background were white, so the background and magic eraser tools didn't get me very far. 

So I moved on to Illustrator. I was able to outline the image using Image Trace, but the best I seemed to do was get a white outline. I'm not sure what kind of paths Image Trace technically creates, but I tried joining paths, uniting shapes, grouping, and the shape builder tool to no avail.

Does anybody have any ideas? I have a feeling there's probably a simple explanation and I'm just not familiar enough with either platform to know the answer.

Here's what the original file looks like (as a jpeg) and here's a link to it if anyone is interested: Hightail

Here's what I've gotten to using Image Trace (jpeg below) and as an ai file: Hightail

Any thoughts are appreciated.

Thanks!