My dealings with CMS have been that they understand the simple 99% of cases, but struggle with the 1%. Things like how to treat ISA income will fall into the 1%; some will refer you on to a specialist in the area, others will just try to make it up as they go along so you will find you get a different answer every time. I would suggest you look up the raw legislation on this, rather than rely on any simplified CMS guide that's aimed at the 99%.
The relevant part of legislation on unearned income (aka stocks and shares) is:
https://www.legislation.gov.uk/uksi/2012/2677/regulation/69
For the purposes of this regulation unearned income is income of a kind that is chargeable to tax under—
(a)Part 3 of ITTOIA (property income);
(b)Part 4 of ITTOIA (savings and investment income); or
(c)Part 5 of ITTOIA (miscellaneous income).
This seems clear that investment income is only relevant where it is "chargeable to tax" - i.e. not an ISA.
However, the rules on notional income (
https://www.legislation.gov.uk/uksi/2012/2677/regulation/69A) a) don't mention ISAs nor b) stop double counting between unearned income and any notional income from that asset.
On the first point, I would try to argue that any notional income ("
The Secretary of State shall calculate the weekly value of an asset by applying the statutory rate of interest to the value of the asset and dividing by 52") stays within the ISA wrapper (in the same way as any interest received on a cash ISA) unless the legislation explicitly removes it from the ISA wrapper - which I don't believe it does.
On the second, google points me to
https://www.legislation.gov.uk/ukpga/1991/48/section/28F - S28F-1b of Child Support Act 1991:
(b) it is [the Secretary of State’s] opinion that, in all the circumstances of the case, it would be just and equitable to agree to a variation.
Its not a get out clause, but gives an argument that double charging is not just and equitable.