offered to reimburse me for it
IANAL, so this is just armchair quarterbacking but, if YOU bought the laptop, it's YOUR laptop. This is assuming the boss doesn't want to tag it as a company laptop in return for reimbursement.
Just because I do work on my home PC (which I do), doesn't mean the company has any right to it.
But, if I figured out the One Great Internet Business Idea or write the Great American Novel and used the company laptop to do it, it's an avenue they could use to claim they own it.
Once again, NAL, but I don't think this gives them an avenue. If the company guys me legal pad and a pen, and I write "[A] Great American Novel", it doesn't give the company any rights to my work. I think you're being a bit paranoid.
Think about everything that would have to fall in line for this to happen:
You'd actually have to come up with an idea or work, worth 'stealing'.
The company would have to know about it AND care enough about it to steal it, or try to claim it as their own.
Would have to prove that the laptop you used was indeed owned by the company AND
That you did the work on the laptop.