Am I correct that when ExifTool lists a certain number for shutter actuations, this is the number since the camera was originally built?
This is very camera specific - the existence, location and definition of the counters vary.
No. Where it exists (eg in Nikon images) the -shuttercount tag is writable and can easily be reset (by ExifTool) to any other number.
Add: If the camera is in your possession and you took the photo and have not modified it, then you can be more certain. But some cameras only count actuations of the mechanical shutter and not the electronic one.