Opinion on business practice related to taxation

I recently went to purchase a watch from a specific EU based company, and noticed something odd in the purchase process. This is a practice I haven't seen in the past, and wanted to get opinions from you all on whether this seems reasonable.

I am outside of the EU, so purchasing products and having them shipped to me typically works like so:

• Find an item I want to purchase, for example, say I wanted to buy this beautiful Stowa marine watch. This is listed as 850,00 € to purchase (and Stowa specifically mentions that this includes VAT).
• Add this to the cart, at which point it will typically show the watch price and the VAT amounts, something along the lines of the following: 

• Set my shipping country, at which point the pricing restructures to remove VAT and frequently increase shipping costs, as I'm outside of the EU:

• Make the purchase, wait for the item to be shipped, etc. 
• Prior to receiving the item, it will go through customs here, and the shipping company typically reaches out to collect local import taxes and duties, as well as a fee to handle the billing (typically around an additional $30). 
  
  Sidenote: being in the US, this is really complicated, and the amount due varies a lot based on how the shipper fills out the customs information. It's always a bit of a gamble on the amount, as the way the customs forms are filled out dramatically impacts the duty rate in the US.
• Pay the shipping company the required amount, receive the watch, and hopefully be happy.😀

Different companies handle this differently. 

Some examples: 

• Chronofactum is great because they list this right in their product pages:

Here you can see, right away, the pricing won't include the VAT when shipped outside EU.

• Formex uses a unified pricing so all customers, in theory, pay the same, but then handles all shipping, import duties, and brokerage fees on their end: 
   

This masks how each portion of the item is being charged (it's less clear what they are charging for the item vs taxes, etc), but is very clear over all.

Now - to my original question - I was interested in purchasing a watch from this company, and they listed the price in Euros, but without details about VAT:

During their checkout process, they add shipping, and show "Tax included" (which is unusual - but I'm thinking that it may be more clear later).

During the checkout process, they specifically break this out to show the "lack of VAT":

Now - something raised a question in the back of my mind with this - so out of curiosity, I tried changing my shipping address to an EU address, and their system does this:

Note that they are showing the VAT appropriately, and adjusting the item price.

I reached out to see if this was a mistake on their part (though it obviously is built into their system explicitly). They have their system setup this way on purpose, and argued that:

We don’t charge vat. We use a standard price for all customers and only pay vat for customers from the EU. This way all customers pay the same price, EU and outside the EU. The only difference is, we pay income tax for sales from the EU.

When I pointed out that they are adding in the VAT but "hiding" it, their response is that "It’s being calculated automatically" as well as "We think that’s the most honest thing to do" (these are direct quotes).

Note also that they are not covering local duties, so purchasing this is really paying them an extra premium (even though they don't have to pay VAT), but then also paying all local import duties and fees here, effectively making the cost of the watch significantly higher.

Now, I obviously see this as an unusual way to conduct business, but wanted to gather opinions from you all. Does this seem reasonable? Am I seeing things poorly by thinking this is odd?