score:1
The UKVI news article you refer to is poorly worded and does not appear to reflect the current state of play with respect to transit visas anyway. It's not in sync with new rules.
The part you are asking about actually reads...
50C. The visa national must also:
(i) be travelling to (or on part of a reasonable journey to) Australia, Canada, New Zealand or the USA and have a valid visa for that country; or
(ii) be travelling from (or on part of a reasonable journey from) Australia, Canada, New Zealand or the USA and it is less than 6 months since he last entered that country with a valid entry visa; or
This is an OR condition which is clear enough when you read the source, despite what the guidance says. The precise definition is given on pages 11 and 12 of the formal Statement of Changes which is here https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/364371/hc-693.pdf
And the instrument itself is here http://www.legislation.gov.uk/uksi/2014/2702/pdfs/uksi_20142702_en.pdf
Note that the Statement and the Instrument sync up with what the lady told you when you called LHR T1...
For reference purposes, I use the most recent guidance they put on the web last Monday, which is here https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/381070/Transiting_the_UK_v11_0_EXT.pdf
Because of these situations where a rule change takes time for the guidance to 'catch up', it is emphatically recommended to carry a print-out of the legislation if you plan to benefit from carrying an exemption document.
Final note: the link you gave in your 'update' leads to a poster (with red and black text and a British flag) meant to hang on the wall for airline personnel to read. It is meant to be used along with the accompanying booklet. Using the poster by itself may lead to undesirable results.