There's all sorts of explanations of what could have happened.
For example, what if the mans blindness was caused by mental trauma, rather than an actual physical malady? The touch and reassurance of a man believed to be holy, being told that he has the ability to see, as a gift directly from God - that could be enough to break through a mental block and allow the man to see again.
Or maybe someone made the whole thing up, or misunderstood what did happen, or maybe Jesus did a minor bit of first-aid for someone with an eyelash in their eye and the story was blown all out of proportion? That's the problem with a book written so long after the "fact" - it's really hard to get the true occurances straight, even if it DID really happen in the first place.
So, in a nutshell...I think your explanation is just as likely (and by that same token, just as unlikely) as any other, including what's written in the Bible itself. *shrugs* You're right...it COULD have happened that way. (And to this heathen, a lot more likely than the miracle explanation)