I think the official link about self sufficiency you studied and then pasted here actually contains inside the reply and solutions over this self sufficiency dilemma. I am quoting the exact wording from same link which give reply:
Exceeding the maximum level of resources to qualify for social assistance:
They will exceed this level if they provide documents showing they have enough resources
to cover their essential outgoings. For example:
bank statements showing savings
evidence of pension payments
receipt of educational grants from overseas
income of a partner, spouse or other family member to which they have regular
access, for example:
o parental funding, or
o a spouse’s salary
a student who is also working may not be considered a worker in line with the
regulations but may provide evidence of income from regular employment in the UK
Moreover, i think if no public funds are being claimed then any balance in bank statement must fulfill the self sufficiency criteria and it is common sense that many of us may have little expenses and can survive on low funds than others.