No. At the moment, when an awarding body (such as a university, or an exam board, or a trade body) issues a paper qualification to an individual, say ABC, they are stating only that the individual known to them as ABC has earned a particular qualification
Even though awarding bodies may ask for proof of ABC’s identity at the time of registration, it is not their role to vouch for that identity to others, and they would not carry liability insurance for doing so.
Rather, vouching for an individual’s identity to others is the role of a specialist service provider, an ‘identity provider’ or IdP. Such organisations look at many factors to determine whether a claimed identity is genuine: evidence of interaction with an awarding body may be one such factor, but is far from sufficient.