I'm not sure about this problem and I found nothing on Alexa.com talking about this problem. Anyone knows exactly that is this true?
If you are looking at it from a marketing perspective where you want to have a High pagerank then you need to focus your efforts on Google / Bing and other important sites. Having a high Alexa page rank is only valuable if you are in the business of selling advertising space on your site. If you are, then maybe QUantCast is a better option for you.
As for the alexa widget, I would assume you can lazy load it if you are worried about performance. Just write a bit of Jquery to append the code after the page has fully loaded. You might be able to use the defer option in the script (does not always work for all code so test it).
Lastly, most of Alexa rankings used to come from the Alexa toolbar. Not too many people install the toolbar, so the rankings are not all that accurate.