That study tells of kids being given a toy for a little while, then revisiting them months later and seeing if they remember what to do with the toy.
For some reason I find that less than convincing, maybe they weren't interested in it, maybe it wasn't significant enough.
Birth is pretty much the single largest event in a babies first year of life trauma wise, I wouldn't be surprised if some remnant of that experience remained because of its intensity and I wouldn't be surprised if a baby remembered the sounds of being in the womb because of the duration of the exposure. Compared to either of those a toy seems to be pretty insignificant and if there is one thing the brain is really good at it is discarding stuff that isn't relevant. Older children that would remember the toy might have been more captivated by it. Babies that I know can be utterly fascinated by some things and completely oblivious to other things, then reverse their interest a while later for no reason that I as an adult can fathom.
Of course the memories of any early experience will fade over time but I wouldn't rule them out so quickly based on this specific experiment, which seems to assume rather a lot about the subjects desire to remember that particular toy and about vision, not memory per se. It's a pretty indirect test.
If something doesn't interest me I won't remember it even today, and I take it as read that my 'long term memory' has been formed by now.
Interesting reading:
http://www.google.com/search?q=do+babies+remember+the+womb
If there is a definitive study that babies can not form memories that could make it through to the age of the OPs child then you'd have to wonder how come babies age 1 can use words and seem to be able to understand some pretty complicated concepts as well as having learned how to use a good part of their bodies musculature, it's not at all rare to have 1 year olds that can walk or even run. If they can do all that without long term memory you'd have to posit some mechanism that allows them to do all this with a memory that spans at most a day. After all, if every day is a new day then you would have to explain the kind of character development you seen in babies during their first year and all this other stuff that I think is definitely memory based without the ability to form long term memories.
Also, vision is a relatively new thing for a newborn, they've seen colours but not actual objects and it takes them a fair amount of time to start to make sense of our 3D world. Sound is different, babies can hear pretty good at a relatively early time during the gestation period (about 5 months in), which means that they then have 4 months to be exposed to their moms heartbeat in a way that they could be aware of it.
Also, you can refresh memories by re-thinking of something that you still remember and you can remember that experience as something by itself, so even with only a shorter term memory you could theoretically carry things over a longer period. Shades of 'memento' there.