No they don't.
You're confusing evidence of an overseas transfer, with the 'source', as in where did the funds you transferred originate from.
The 'source' would be a pension letter or statement from your overseas pension provider, or similar, and that does not appear on an overseas transfer.
My IO require a 12-month Thai bank statement with evidence the transfers originated from overseas. (Coded FTT, International, credit advice receipts, or a foreign exchange transfer form).
For extensions based on retirement using the income method, they also request evidence of the 'source' of those transferred funds, such as a pension letter/statement, similar to what those who can obtain an Embassy Income letter have to provide to their Embassy to obtain the letter.
Not all Immigration offices will request evidence of the 'source' of the funds in your foreign bank account, but be aware they can.