I think it's partly about expectations.. 10 years ago you could throw any old clunky website up and people would accept it if the product/service was ok. Nowadays it's pretty uncommon to meet a design free website, especially for something you might buy, so the bar has been raised.
To my mind, you have to treat MVP as a full commercial release, including:
- professional looking website and sales process, appropriate for your target market
- professional looking support and pre-sales processes
- bug count - "reasonable" - ok, you can't go for bug free, but I don't think you should be throwing junk at the market either - that can kill you. You shortcut this at your peril.
- reasonable level of help and FAQs that should have come out of early beta/trialling
In other words it's a way to get moving and building volume, not a way to do 50% of the required effort. On the strength of that, it should be a product not a demo or proof of concept.
All of these items and processes will be needed in some form as further releases are made, so you need the full set to start to test whether your assumptions on market, website, support volumes etc are correct.