" because I know downloading games you own from other sources (torrents) is illegal, even if you own the game."
That has not yet been established from what I have seen, just seems to be commonly echoed around the place in such discussions.
Torrents would probably mean uploading it as part of it all and that would fall under distribution, however the argument that simply downloading something you own a version of has not been established from what I can see. Most cases which established precedents have involved personal backups/format shifting (
https://w2.eff.org/IP/eff_fair_use_faq.php has a tiny bit more) but if they are sitting there trying to figure out how you might have harmed them (it is civil law, not law of the land, civil law is all about harm done to other parties) then that is not as clear cut -- so you owned a copy at the time, it is the same as your copy, the owner did not pay anything to distribute it to you, you did not distribute it as part of obtaining it... hard to see where the copyright owner lost out there.
Likewise softmodding a console, depending upon how it is sold/made/used anyway, may be unlawful in some capacity. The US has a horrible piece of law called the DMCA and that prevents people from bypassing software protections in devices, though there are an increasing number of exemptions (
https://library.osu.edu/blogs/copyright/2015/12/30/new-dmca-exemptions/ ). As far as I can see said exemptions are quite narrow (everything there sounds like an embedded device, I might employ someone different to make the UI but the underlying stuff I would employ the same person to do) and do not include game consoles as they are typically defined, if said console was like the PS2 and PS3 and came with Linux or something to make it a general purpose computer (usually then attracting a different tax rate) then that may be different. Certainly mod chips and flash carts seem to get smacked down time and time again in the courts, and softmod or not has little bearing on any of that.
Re "so this doesn't not breach a law, correct?"
I don't know, the thing with the bandwidth and the cost of services for that would be the legal side of things I look at. If they can demonstrate you accessed their servers/services without authorisation, possibly even bypassing a protection (presenting it with the ticket is functionally not a lot different to using an authentication token incorrectly) and downloaded a file, thus costing them bandwidth, it could probably be argued you cost them the bandwidth. That is thus "obtained services by deception" or simple "theft of services", hence my mentioning those in the opening of that. If Nintendo provide such an option for you moving to a new console, or deleting it to restore later when you have more storage then investigating this is rather more tricky so there is also that.