[lawtalkinghuman]

Yes, that's the general rule.

You then get lots of interesting exceptions and difficulties in applying that rule: who pays when you have multiple potential defendants (but some of them have died or gone out of business or are in a different jurisdiction), or there are fiddly causation issues, or the defendant is an organisation that's vicariously liable for their employee/contractor/authorised religious leader/any number of other relationships, or there's insurance involved, or there's some third party interest, or the purportedly tortious act was mandated by some law or other obligation, or the government decides to set up some kind of alternative process of compensation which may or may not indemnify the tortfeasor, and so on and so on.

When dealing with the not-so-straightforward cases, appellate courts do look at questions like "is this a fair and equitable distribution of the cost?" and legal scholars compare the pros and cons of tort liability to other mechanisms (compensation by the government, industry self-regulation, no-fault/strict liability, mandatory insurance etc).