Year 6 SATS are definitely Age Standardised. The above QCA document actually says so, there is a whole section which explains why they age standardise.
The reason for the comment
"Age standardised scores do not affect the pupil’s test levels."
is just a reference to the fact that they take it into account when setting the level.
If you print out the document you will notice that the Age Standardisation tables have diagional greyed out areas (where the grey band age standardised scores increas slightly with age).
If you print of the document and take it to the teacher they will be able to see that the information they gave you last year was incorrect.