From the fine specification:
p – paragraph
[…]
Permitted contents
Phrasing content
And what is this Phrasing content?
Phrasing content:
Consists of phrasing elements intermixed with normal character data.
Normal character data is just that: unmarked up text. Phrasing elements are:
a or em or strong … [a bunch of other elements none of which are div]
So, <p><div></div></p> is not valid HTML. Per the tag omission rules listed in the spec, the <p> tag is automatically closed by the <div> tag, which leaves the </p> tag without a matching <p>. The browser is well within its rights to attempt to correct it by adding an open <p> tag after the <div>:
<p></p><div></div><p></p>
You can’t put a <div> inside a <p> and get consistent results from various browsers. Provide the browsers with valid HTML and they will behave better.
You can put <div> inside a <div> though so if you replace your <p> with <div class="p"> and style it appropriately, you can get what you want.
Your reference at about.com disagrees with the specification at w3.org. Your reference is misleading you.