It could totally happen. Acceptance usually has more to do with research fit than anything else so if you fit better with the higher ranked school then you will be more likely to get in there. I think it also has to do with the professor's "rank". For example, there are many ivys that I would never consider applying to because their professors arent as well know as i would like while there are many professors at top 50ish ranked school who are basically celeberties. My chance of getting in with the celebrities is probably much lower than with the unknown ivy professors.
Could also be a matter of the quality of statements, writing samples, etc. If a lower ranked program has an earlier deadline, you could easily submit documents that are just not as polished as those submitted to higher ranked programs with later deadlines.
I don't have data for all programs on average, but I can tell you what I did to try to figure this out for my own field (computer science):
I made an Excel spreadsheet with a row for each week, and counted up, for each of the schools I applied to, the number of acceptances/rejections to both MS and PhD programs in that week. I then divided each number by the total number of acceptances/rejections for that school -- so for each week I could see what percentage of a school's responses were sent out.
I found that there are two waves: one that ends around the end of February, and one that starts and ends from the middle of March until the middle of April. This second wave tends to be mostly acceptances to MS programs, "consolation" acceptances (giving a nonfunded MS acceptance to someone who applied to a PhD program), or just a flurry of rejections as afterthought.
Comparing the results and filtering out MS programs and then rejection responses, I feel relatively confident that if I haven't heard anything (interview or acceptance) from a school to which I applied to a CS PhD program by the end of February, I most likely will not be accepted there.