The shape of the quotation marks is subject to the will of the font designer, like all other glyphs, so long as the shapes are distinctive and carry out their standard meaning.
In the case of Palatino, which PXfonts is based on, designed by Hermann Zapf in 1949, some shapes are quite peculiar; for instance, the “f” does not extend past its bounding box, like in the majority of fonts.
I used newPX fonts, which are actively maintained, whereas PXfonts aren't and have several weaknesses.
If you look at the quotes in context, you'll see that they do their job. They're just different from the quotes in Times.
There is no “standard” shape for any glyph, apart from general templates which the font designer develops on. You can like or dislike them, but a font design is “global” and Zapf decided for that shape of the quotes after looking at the whole font. He wanted a “new” design, so it can happen that an eye accustomed to “classical” fonts deems that shape “wrong”. It isn't.
The same test as above, but with quotes taken from Times, would output
You can clearly see that such glyphs don't fit with the global design, that has no bowls at all.