I think sometimes the speaker feels (wrongly) that the obvious pronouns such as "me" and "you" are a bit too direct or perhaps even childish - it’s interesting that this rarely happens with the third-person ones such as "him" . It's a bit like saying "Your Highness" "Your Lordship", etc, which avoids the over-personal "you". Using them as emphatic pronouns (e.g. "I haven't seen him myself") is correct, but using these forms as stand-alone substitutes for regular pronouns ("Please hand the forms back to myself or my colleague") just sounds silly. If you can say "me" instead, then do so.
The media are already after Andy!

as in "you can speak to myself or to Miss X"


