While your theory has some logic, that is not the law. The non-attorney of record's fees is a factor. If you want citations, you should retain an attorney to help you to help get you out of this.
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Your question assumes fees are being claimed by "attorneys." California statutes generally authorize fees to be claimed by a "prevailing party."
Attorneys, with client consent, can use outside counsel to handle a case. If it takes 10 hours to successfully represent the client, with 7 being expended by the attorney of record and 3 by some other attorney, why would the client not be able to request an award for 7 hours at a reasonable rate for attorney 1 and 3 hours at a reasonable rate for attorney 2? Why should the losing party (you) obtain a windfall by paying something less than reasonable fees? Perhaps you even agreed to do so in a contract.
You may wonder whether a claim can be made for more than the attorney is charging the prevailing party. Sure. The statutes provide for "reasonable" awards. What is more, even though the courts won't allow self-representing litigants to claim fees on grounds they did not "actually incur" the fees, in other circumstances cases indicate the claimants need not have "actually incurred" the fees. If the rule were otherwise, the purposes of the statutes would generally be subverted. Thus, homeless people who are represented "pro bono" may, upon prevailing, apply for fee awards. Similarly, organizations represented by in-house counsel can seek fee awards at reasonable rates even if they only paid their attorneys on a small annual salary basis.
If you are trying to defeat or minimize a fee award, it might be cost-efficient to hire someone who specializes in the area and pay for an expert.
These remarks constitute general information, not legal advice. I am not your attorney unless you have entered a written fee agreement with me on a form provided by me.