I'm confused - an invoice is just a statement of what is owed. It isn't a formal legal document. So I'm not sure what their setup has to do with it, or what you mean by "has zero legal value"?
In all EU countries an invoice (tax receipt) is a legal document very exactly specified by local law as well as EU regulation, and you can't move a cent without it - you won't be able to claim the expense (subtract from tax base = pay income tax on profit only) if you don't have it.
I'm an American working for an Italian company as a freelancer, and I just print a generic invoice from Harvest (time tracker). I've also seen us pay other freelancers who make simple PDF invoices from web templates.
Have we been doing it completely wrong this whole time...?
No, you haven't done anything wrong. Some people are just paranoid-compliant to the maximum level. Unless a company is doing actual money laundering or financing terrorists, the tax auditors won't give a damn about some wrongly formatted invoices from freelancers, as long as they are based on reality.
Ok, phew, thanks for the reality check! We don't finance any terrorism (unless you count the quality of my code). We're just a small company without a big legal/accounting dept.
PDF invoices are nothing wrong. As long as you're not a VAT payer there are just basic requirements (vendor/customer ID and address, invoice number). Most likely yours is compliant - but you need to provide it.
In some of them a "tax invoice" is indeed an official legal document.
In some countries the format of the invoices is highly standardized and regulated, and even an invoicing software has to be certified by the tax authority.