I don't see anything wrong with putting shitty tp in the trash can....We have a septic tank and we put all tp in the trash can out of necessity. If you have ever had a septic tank back up, then you will know what I am talking about. Tp is biodegradable but that doesn't happen overnight...
Now if you live in the city then you are connected to the city sewer, so you have nothing to worry about, but in the country we have septic tanks & you NEVER want one to back up on you....