In my experience with the Greek language, lower-case pi is most commonly written with the top line extending to the sides in print. It may be written as the plain figure version that Arial is using, or the more stylized version commonly known from math, but rarely as a small capital pi. However, as noted in previous answers, this is still an acceptable form of the letter, especially in hand-writing.
The question still remains, why this choice was made. My theory is that for whatever reason, the designer of Verdana preferred to have similarities between certain characters between Greek and Cyrillic. As evidence, I present a couple of other characters where this pattern appears.
As a reference, here is the aformentioned Greek lower-case pi (U+03C0) and Cyrillic lower-case pe (U+043F) in Arial:
Here are the same characters in Verdana. The glyphs are identical:
Here's Greek lower-case kappa (U+03BA) and Cyrillic lower-case ka (U+043A) in Arial:
Here's the same two characters in Verdana. While the glyphs are not identical, kappa has a slight curve at the top, which for Greek is only commonly seen in serif fonts, whereas it is ubiquitous in Cyrillic:
Lastly, Greek lower-case tau (U+03C4) and Cyrillic lower-case te (U+0442) in arial:
...and Verdana. In Arial, the roof of tau is less wide, which is common in Greek, whereas in Verdana, the glyphs of tau and te are identical. While this is easily justifiable from a readability point of view, this is nevertheless another example of a case where Verdana uses an identical glyph in Greek and Cyrillic when it's not obvious that it should: