I don't know too much about their status
but if your solicitor told you then I will go with his advice. I found
something at Home office site and according to that they (BOC) are still
considered person with ILR because of the conditions applied on them. Like
they can apply for citizenship after 5 years and they should not be out of the
country for more then 450 days and so on and on...
In my un-experienced opinion and common sense tells me that you will need to
take the test. I might be wrong but I think you are not considered British
Citizen until you fulfils their 5 years requirement.
Here is the link and text, you can read it your self:
http://www.ind.homeoffice.gov.uk/applying/nationality/advice/bn2
Registration as a British citizen
9. If you are a British Overseas citizen, you are entitled, on applying, to be
registered as a British citizen after you have lived in the United Kingdom
for five years (see Note F). You may be absent from the United Kingdom for up
to 450 days during this period without losing your entitlement to be
registered, but you can only be absent from the United Kingdom for 90 days
during the year immediately before you apply. The Home Secretary may accept
longer periods of absence in the special circumstances of a particular case.
You will normally have to be free of restrictions under the immigration laws
throughout the year before you apply.
I think other people in your situation might appreciate if you can keep us
posted after finding out more.