But don’t they have a tray on the bottom that collects crumbs? Then is pulled out to empty/clean?
It's a feature of modern toasters, along with electronic timing, to replace the bi-metal (toast done) trip - and a lever to lift the toast out to reverse it, without turning the toaster off. The latter addressed the problem of the inner side of the toast, to the toaster, browning faster the outer side.
Tilting on it's side, would not affect either of the toaster types I have ever used, though I have never used one on it's side. What I would expect, is the toast face over an element to brown much faster, and maybe burn - heat rises.
Tilting a full tray might distribute enough crumbs to catch fire and operating on it’s side might prevent the auto off function.
In the days when they lacked a removable tray, I used to simply unplug, and turn the toaster upside down, over a bin, and tap it, to dislodge the crumbs. I still do similar, with the modern ones, after emptying the tray.
Fires rarely start instantly, unless there is something highly combustible about, they take time to develop, with usually a strong smell of burning preceding the actual fire. That, alone, suggests the toaster must have been left unattended for several minutes. Hence, I would suggest it must be the tenant's fault - no one should leave such an appliance unattended.
