Prospective tenant with dodgy references

AND, … take a Guarantor. ( and reference them also - obviously )

Well if the tenant claims to be earning that much, he/she would argue no rent guarantor is needed.

I’d say follow your gut feeling. Worst case, take the tenant on, do reference and if you use Alan Boswell landlord insurance, you would be able to purchase rent guarantee insurance and legal cover cheaply. Good luck