Not sure if the BBC is saying travelling does not count as exercise or if folk cannot travel and then exercise. If it's the latter, that is not correct.
The Welsh Regs state,
"(5) In sub-paragraph (4)(f)[allowing exercise]—
(a) exercise must start and finish at the place
where the person is living or where a member of the person’s extended household is living,
or
(b) where, for reasons of physical or mental
illness or impairment, or a disability (within
the meaning of section 6 of the Equality Act
2010), the person needs to exercise in another place, exercise must take place in an area local to the place where the person is living."
That means those with a physical or mental
illness or impairment, or a disability can travel and then exercise elsewhere.
Folk can also travel to wherever a member of their extended household lives and begin their exercise from there.