I can't think of a single case where that's been true, in either my experience or anyone else's.
The contract language comes into play when everything has already gone to hell. Yes, there needs to be a contract. But you should never assume it will give you any particular leverage over a larger, well-represented client who has elected to take an adversarial position.
The above is clearly a situation where contract verbiage for transfer of rights would make any subsequent conversation on the topic very short. However, as to your general point, what do you suggest? Is that risk something that can be mitigated, or priced into your rates?
There were already lawyers working for both parties before they signed the contract. Nobody has to find one just because there was disagreement.
One of the things I've learned from Patrick Patio11 is that negotiations should be on scope not price. The implementation is that clients who expect me to deliver something they cannot afford aren't worth taking on.
This should include the work to be performed, payment schedule and penalties for late payments (which are generally covered by usury laws, the workaround is often to offer a discount for early payment), what copyrights are transferred and when, responsibilities for providing assets, acceptance criteria, liability for defects, severability, and controlling law. Non exclusive list written from memory, IANALATINLA.
Relationships may be important, but that does not mean automatically getting screwed if the client decides to. A well-written contract protects both parties. We need contracts because this isn't a perfect world, things go wrong all the time, and it's very easy to burn relationships unless you both agree about what to do when things go wrong, before the lawyers start getting involved. And again, if it does get to the point where the legal letters start flying, without a contract you are going to be severely limited in terms of recourse.
Another way to look at it is that without a contract, you are both taking on risk; the risk of not being paid is probably the biggest factor. If you can avoid a $5k to $50k risk by spending a few hundred dollars, why wouldn't you?
If you need more than my words to convince you, I suggest either reading clientsfromhell.net, or watching "Fuck you, pay me." http://vimeo.com/22053820