False. Again, in the US:
1.If you're contracted for a specific project then IP ownership defaults to the customer. This has been upheld for everything from traditional engineering projects to software to literature.
2. If you're on a regular long-term/time-based contract then IP ownership defaults to you, however, the customer retains "shop rights" to use/reuse anything developed at no additional cost.
3. You have no IP rights if you violate another's. if your IP uses somebody else's IP, you need a limited waiver of their rights to claim yours. Similarly, you cant claim sole ownership of IP that was codeveloped. Most contract engineers dont work in a bubble, we usually start with another's IP and receive regular feedback/input throughout as our work progresses, so need a detailed contract acknowledging others' IP to retain our own, not general/proforma/copy-paste terms.
I gave several examples where suppliers can be held liable for rework in a previous post - gross negligence and partnerships/JVs. Generally tho, they're only liable for a refund and cannot be forced to pay for the cost of rework/damages. Bc of this, at some point in our careers most of us have had to tell management that we chose a supplier who did lousy work, and that our employer had to eat large rework costs.