Only if one assumes that the lower port has none of the higher ratings features...The fuel comment I made was intended to highlight that regular merchant traffic is unlikely to take the risks to travel to worlds with no refined fuel available. The scout/courier can make such trips with no issue.
Which begs the question of how C starport worlds attract civilian ships - they will suffer from unrefined fuel use eventually.
C ports would need all the B port facilities to be rated B; lacking any of them (banking, small craft construction, TAS Hostel, refined fuel) means it's still a C port. If Xyzzy for some reason loses it's TAS Hostel, TAS, at least, will list it as C.... it it has no yard, it might have all the others, but the IISS and IN will still list it as a C Port.