In this link under " How to pay tax on the remittance basis" it is says that if you choose the remittance basis and have more than 2000 in earnings outside the UK you have to file a return.
Under "Allowances and reliefs if you don't choose the remittance basis" it lists a whole lot of stuff, and the last entry says you have to file a tax return.
HMRC website is for guidance only; it is not the law. As a consequence whilst helpful it is not exhaustive and to some extent can be either misleading or in fact completely incorrect as the last sentence quoted above.
The £2,000 to which your colleague referred is as per my earlier posting outlined which in any event does not appear to apply to you on your figures which each tax year show unremitted foreign income/gains of more than £2,000.
In short my earlier postings stand.