Regulation 60 establishes the rules regarding the means of proof that contracting authorities may require economic operators to provide attesting their capabilities or compliance with requirements. As Albert said, the means of proof are regulated in minute detail in Regulation 60 and are limited to the ones contained in it as well as Regulations 58 (selection criteria) and 62 (quality assurance and environmental management standards).
I find interesting the lack of articulation between this Regulation and the preceding one, bearing in mind that the EPSD (and the fact-checking contained herewith) appears to be the preferred method for dealing with qualification and selection. However, paragraph 1 of Regulation 60 states that "Contracting authorities may require the certificates, statements and other means of proof[...]" (emphasis mine), thus indicating a discretion in the possibility of requesting the means of proof mentioned in this Regulation. How do we square this circle then? Maybe these elements of proof (which sometimes are confused in the UK with selection criteria...) can be mentioned at the start of the procedure and can be covered by the EPSD until if and when the contracting authority requests the originals? This would mean, in first instance, the contracting authority going through the motions of finding these elements if they are on a public database and only afterwards request them directly from the economic operator.
The Regulation is divided into three parts: proving the absence of grounds for exclusion, proving economic and financial standing and proving technical and professional ability. The rules are quite prescriptive and detailed for each section or category, leaving limited scope to the contracting authority to be inventive in the documents it can request to attest any of these capabilities.
In any event, there is enough detail there for a contracting authority to drill down into most characteristics that may be relevant for the qualification/selection "job to be done" (ensuring they are not hiring a lemon)