I don’t think this discussion was concerning upgrades being performed by a SY of another race.
If you build your own T1 SY, it is certainly plausible that you’d have the technology to upgrade modules on your own ship at your own SY, though at a slower pace due to the limited number of workers available. Remember, you already have the technology for all the modules you might use in upgrade. Remember only the hull itself is limited to being built in the SY, not the modules and in an upgrade you are not changing the hull, only the modules in it’s design.
As for other race’s SY, if you aren’t able to perform an upgrade to an existing ship at another race’s SY, why would you be able to build an entirely new ship there even at the limit of the captured race’s SY level? I don’t think you can have it both ways. Though building ships at another race’s SY is now allowed, I actually think this should be changed and when you capture another civ’s SY, you should be required to do a conversion upgrade (not dismantle and start from scratch) to the SY itself so it becomes compatible with your technology. This might also be more realistic if applied to other technology based structures as well, such as research labs.