csa payments and apprenticeships?

Most apprenticeships nowadays do not meet the criteria to be classed as full-time, non-advanced education or approved training.

If the apprenticeship is paid for by an employer, it's not approved education. If he is paid as an apprentice, it's highly unlikely to be approved training. Additionally, if it's in England (rather than Scotland, Walea or NI) it's also highly unlikely to be approved training as defined for child benefit/child support even if unpaid.

As mentioned before in past threads, it's unlikely the decision in your case was correct if it was an employer provided, paid apprenticeship.
http://www.aviva.co.uk/life/family-life/article/child-benefits-apprentices/
https://gingerbread.org.uk/content/779/When-your-child-turns-16
https://gingerbread.org.uk/content/2160/Ask-an-Adviser-January-2016 question 13

The guidance you linked to specifically includes the points I highlighted above.

This is the Child Benefit Technical Manual as used by HMRC to make such decisions:
https://www.gov.uk/hmrc-internal-manuals/child-benefit-technical-manual/cbtm07020

I've copied below the relevant sections:

CBTM07020
Prescribed conditions for a child or qualifying young person: Education and training condition
Child Benefit General (Regulations) 2006, regulation 3

A person who has not attained the age of 20* is a qualifying young person if they are:

• undertaking a course of full-time education, see CBTM07022, which is not advanced education, see CBTM07021, and which is not provided by virtue of their employment or any office held by them which is:
  provided at a school or college; or
  provided elsewhere but is approved by the Commissioners**;
  part of a Study Programme in England from Sept 2013***
  
• undertaking approved training, see CBTM07024, that is not provided by means of a contract of employment, or
  
• having undertaken one of the above courses has been accepted or is enrolled to undertake a further such course.

*A person who is aged 19 is only a qualifying young person if they began or were accepted/enrolled on the course of education or training referred to above before attaining that age.

** A person is not a qualifying young person if they undertake full time non-advanced education somewhere other than at a school or college unless they received that education (as defined in the first bullet above) as a child at a place other than a school or college.

*** Study Programme - From Sept 2013 all students in England aged 16 to 19 will be doing a Study Programme. Study programmes include traineeships (in England) and foundation learning. These are to be treated as full-time non-advanced education without the requirement that they be undertaken at a school or college.

CBTM07022
Prescribed conditions for a child or qualifying young person: Education and training condition - Meaning of ‘full-time education’
Child Benefit (General) Regulations 2006, regulation 1, (3)

Full-time education is education in pursuit of a course where an average of more than 12 hours per week (term time) is spent on the following:

• receiving tuition,
• engaging in practical work,
• supervised study,
• taking exams.
  When calculating the 12 hours do not include time spent on meal breaks or unsupervised study.

CBTM07021
Prescribed conditions for a child or qualifying young person: Education and training condition - Meaning of ‘advanced education’
Child Benefit (General) Regulations 2006, regulation 1, (3)

Advanced education means a course of education which is:

• above the equivalent of level 3 on the Qualifications and Credit Framework (QCF) in England, Wales and Northern Ireland - level 3 being the equivalent of GCSE A level, or
• above the equivalent level 7 on the Scottish Credit and Qualifications Framework (SCQF) in Scotland - level 7 being the equivalent to Higher National Certificate
  For example
  
• a degree or a preparation for a degree (eg. a foundation degree),
• a diploma of higher education,
• a higher national diploma,
• a teaching qualification
  Note: Any course that is not considered advanced is considered non-advanced.

CBTM07024
Prescribed conditions for a child or qualifying young person: Education and training condition - meaning of ‘approved training’
Child Benefit (General) Regulations 2006, regulation 1, (3)

‘Approved training’ means arrangements made by the Government:

• in relation to England arrangements made by the Secretary of State under section 2 of the Employment & Training Act 1973. This is currently:
• ‘Access to Apprenticeships’
  Note: From September 2013 ‘Foundation Learning’ is treated as a study programme under full-time non-advanced education.
  
• in relation to Wales arrangements made by the Secretary of State under section 2 of the Employment & Training Act 1973. These are currently:
• ‘Foundation Apprenticeships’ or ‘Traineeships’
  
• in relation to Scotland made by the Scottish Ministers under section 2 of the Employment and Training Act 1973, or by Scottish Enterprise or Highlands and Islands Enterprise under section 2 of the Enterprise and New Towns (Scotland) Act 1990. This is currently:
• ‘Employability Fund’
  
• in relation to Northern Ireland, made by the Department for Employment and Learning under section 1 of the Employment and Training Act (Northern Ireland) 1950. These are currently:
• ‘Training for Success: Professional and Technical Training’, including ‘Programme Led Apprenticeships’, ’Pathways to Success - Pathways for Young People’ and ‘Collaboration and Innovation Programme’.

Links to info on Study Programmes:
https://www.gov.uk/government/publications/16-to-19-study-programmes-advice-on-planning-and-delivery
https://www.gov.uk/government/publications/post-16-work-experience-as-a-part-of-16-to-19-study-programmes