I am an immigrant founder (from India) and part of the YC summer batch of 2011. I think PG's statement has definitely been taken out of context and blown out of proportions.
I did have a foreign accent but thankfully not so thick to make it non-understandable. I received a similar feedback from PG before the demo day and I worked on it.
As an entrepreneur, you can do two things - either take it as an insult and leave it or as constructive feedback and work on it. In fact, I setup an office hour with Garry to just work on this.
For eg: in India, the word programmer is pronounced as prograamar (the stress is at the end) vs pro-grammar in US. And similarly, path is pronounced as "paath" as opposed to "p-a-th" (stress on 'a') here. These are definitely minor things that you have to tune (and I'm sure PG was referring to a much more thicker accent people had) which will make it easy for people to follow what you are saying.
If you didn't work on this, the investor would miss what you had said and then after a couple of seconds would realize.. "oh. you said programmer, okay", the train of thought is lost, you continue with the slides and it repeats again. And that's not okay.
After you have identified a product-market fit in your startup, I have realized everything is about convincing, every damn thing.
-- convincing the guy to join your company
-- convincing the customer to buy your product
-- convincing a new investor to make a bet on your company
-- negotiating/convincing for compensation and pay package
-- convincing someone to continue to stay in your company
and so on..
It's almost like I can prefix a huge percentage of my work with the word "convincing" and it would all make sense. When that's the case, it's better to ensure at least your statements are eloquent and of high clarity that doesn't require repetition (unless of course the person wasn't listening). You are just going to improve the odds and that's what a startup is all about - do things that increase the odds of success.
It's a constructive feedback that I believe entrepreneurs should work on for their own good. It's not equivalent to sounding like an american but if you have a foreign accent (which you will if you aren't born here), please work on it to ensure what you say comes off clearly. That's it.
And YC clearly has no bias based on accent. I know tons of immigrant founders who are part of YC. In fact, 3 of my classmates (all from India) are a part of YC.