I doubt that there is an actual rule as you describe. In scientific circles, many people typeset their work using the LaTeX typesetting engine because of its good support for mathematical equations and so on, and because it sort of adheres to a principle of separating design from content.
The LaTeX typesetting engine uses the concept of image and table floats which automatically try to determine the best position for your figures and tables and "floats" them to that position. The default (which some publishers insist on) is to have the float setting be
tbp which basically specifies the order preference for placement of floats as being either:
t = at the top of page,
b = at the bottom of page, and
p = on a special page just for floated elements.
The downside to this default is that sometimes figures and tables appear before they are mentioned in the text on a page (if LaTeX decides the best position to place the float is at the top of the page). My personal preference is to avoid this behavior. Of course, these settings can be overridden (for example, adding an
h, making the float statement being
htbp, changes the default placement to first try placing the float "here", before trying the other three options to determine what is best) but since part of the idea behind LaTeX in the first place is "you work on the content, the program will figure out how to make it look good", I suspect that there are a good number of people who just leave the default settings as they are.
Given your preamble that "I have to write a scientific paper for a university course. As far as I know, and as far as I have ever seen, tables and figures are always inserted at the top of a page", the widespread use of LaTeX to typeset journals, books, and working papers might be an explanation for your belief.
However, if you spend some time looking into this question further, I am fairly convinced that you will find more people recommending closer integration of text and figures or tables. You argued that placing figures and tables at the top of pages "keeps the text together and more readable". However, most argue the exact opposite, saying that if the reader has to turn the page to look at a table or figure (or even look down to the bottom of the page to read a footnote!), their concentration is broken and increases the reader's load.
Perhaps one of the most prominent advocates of that alternate style (placing figures and tables as close as possible to where they are mentioned) is Edward Tufte. Below is an example of a page where he describes this feature, using Galileo's work as an example. (Note also how his "footnotes" appear directly in the page's margin.)
Anyway, to wrap this up, I would say you might want to do some more investigation before you decide on your own standard; or, if you have to submit to a particular journal or publisher, contact them and ask what their standards are (most will be able to provide you with author guidelines for manuscript preparation of some sort, perhaps even a template). This will save your group time arguing over matter of style (things for which there really aren't rules) and let you focus on your content.