For Australian and US pensions they are specifically mentioned in the DTAs as being taxable only in the country in which they're paid. Very cut and dried. Tax credits don't even come into the equation.
It says "the whole thing has been a mess". That's total bs. If the OP is so frightened (or perhaps has money hidden offshore) that he/she will leave the country, there's some pretty strange "voices in the head" material going on.
Not all. Some countries such as Australia and USA, pensions are taxable ONLY in the country in which the pension is paid. Tax credits don't come into it. It's cut and dried