Zero rate is a rate of VAT, a seller who zero rates their sale (such as printed matter) is making a taxable (VATable) sale, that sale is subject to VAT, it just so happens to be the rate of VAT is zero percent.
Zero rate is entirely different and not the same as "not charging VAT".
Partial exemption relates to a business which makes both taxable supplies (zero, reduced, standard) and also exempt supplies (welfare, insurance, finance, etc).
With zero rate, you are charging VAT, albeit at 0% and you are entitled to reclaim your input tax on costs...because you are charging VAT, you are making a taxable (VATable) supply.
With exempt sales, you are not charging any VAT at all, and because no VAT is being charged then you are not entitled to reclaim any input tax on your costs. A partially exempt business, which makes both VATable/taxable sales and exempt sales has to perform a partial exemption calculation to adjust what amount of input tax they can reclaim.
In terms of expenditure then, if you buy in goods which are zero rated or exempt then there is no VAT for you to reclaim. For example, you buy a pack of stamps for £5 from the Post Office, this purchase is exempt because postage stamps are exempt, Post Office is not charging any VAT on these stamps and so there is nothing for you to reclaim either.
You cannot reclaim VAT on purchases where VAT was not actually charged by the supplier/seller. But are you sure "hardly anything we buy is standard rated?"....Do you not buy in plain paper, card, inks and dyes? These would usually be standard rated purchases. Do you have a printer in the office? Do you have a cutting machine that trims paper? These machines will be standard rated when you buy or lease them. You should be able to reclaim the VAT on these purchases as long as you have a VAT invoice from the supplier and the invoice clearly shows net, VAT, gross on the invoice.
In your quote "A zero-rated VAT item is an item that falls within the VAT scheme but the VAT charge is 0%. So reclaiming VAT on zero-rated supplies is still an option if you’ve bought things necessary for your business that year." what that is saying is what I've stated earlier, zero rated sales allows you to reclaim input tax on purchases related to the zero rated supplies (sales) you have made, but of course you have to actually incur input tax/be charged VAT by your suppliers in order to reclaim VAT.
I'd have thought a typical printer business would be in a refund position most quarters as there is no output tax due to HMRC (all sales zero rated) and any input tax on purchases is recoverable.
Your Accountant appears to be correct in saying that you cannot reclaim VAT on purchases which are zero rated. How can you reclaim VAT when there is no VAT showing on the purchase invoice? I suggest you go back to your Accountant and ask them to explain in more detail as to what VAT your business can reclaim.
To reiterate, you can only reclaim VAT where it has been incurred/charged by a supplier and shown on the suppliers invoice.
the partial exemption £7,500 you refer to is saying a partially exempt business can reclaim input tax in full if it is under the £7,500 threshold but that business still has t incur VAT being charged to it by suppliers. if the business buys all of its goods and services from non VAT registered traders, then a partially exempt business as no input tax to reclaim at all, the £7,500 is irrelevant as there is no VAT being incurred by the business.
saying you can reclaim VAt if it is under £7,500