No it isn't.
First, the BBC disagree with you about t being a separate grant. They think S4C is partially funded from the licence fee.
S4C is indeed partially funded from the licence fee, but it's still a separate DCMS grant to one to the BBC. You may be getting confused by the government letting licence fee collection out to the BBC Licence Fee Trust, who collect it under names like "TV Licensing Authority" which Capita and friends do much of the actual work/bullying for, as described in earlier posts. The income still goes into government funds and then DCMS uses it to fund grants to broadcasters.
You can see the grants in the DCMS accounts (figures are in £thousands):
Second, they have a strategic agreement for cooperation, with the BBC providing at least 520 hours per year of S4C content. While some BBC Studios content is bought by other broadcasters, that is not close to the same level of cooperation.
And S4C content is all available on iPlayer. No other broadcaster has that.
I expect BBC would host other Public Service Broadcasters if the price was right or it made sense to them. Broadcasters often make strategic agreements, whether that stops at cooperation or results in merger or takeover, but it doesn't make them the same corporate family until then.
And they share the broadcasting centre in Cardiff.
https://www.bbc.co.uk/aboutthebbc/governance/s4c
So they sublet some space. BBC Look East broadcasts from the central library building in Norwich, but that doesn't make them part of the Norfolk County Council family. S4C's HQ is in Carmarthen not the Cardiff studios. That's an even weaker argument than S4C being in "the BBC family" because BBC currently collects the licence fee that funds it.
So, I feel the only way that the original claim:
None of the channels outside the BBC family get any funding from the licence, regardless of nationality.
is true, is if you redefine the BBC family to include all channels funded by the licence fee, which seems rather circular and not what's generally seen as a family of companies.