Yes, but unless Shopify have changed things in the last month it means that your client is charging the VAT inclusive price to everyone, including customers where VAT wouldn’t be charged, because that’s what that setting controls. In essence - international customers would be charged 20% extra.
For example - with that setting unchecked, with a client based in the UK selling internationally:
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Product A is £30 in the backend, with “Charge tax on this item” switched on
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Customer A in UK buys it, they pay £30 with £5 of the price (20%) being VAT - OK.
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Customer B outside UK buys it, they pay £30 with £0 of the price being VAT - NOT OK.
Customer B has been overcharged 20% relative to Customer A. Customer B should only have paid £25.
So, you’re both right and wrong in my opinion. Unchecking that option does result in the same price being shown to everyone, but it also results in the same price being charged to everyone, which is not what we want.