If your deceased Uncle had an attorney (now the living Uncle's attorney), then presumably that attorney would know whether there was a will drafted. Since they are applying for letters of administration, they are saying no will exists.
The verbal wishes of your Aunt and Uncle carry no weight unless, in objecting to the administration, you can convince the court that a will was written, signed, and properly witnessed. Even if such a will existed, the fact that it no longer exists will create a rebuttable presumption that it was destroyed by the decedent. And remember - you're looking for TWO wills - that of your Aunt and that of your Uncle.
In the absence of wills, the verbal statements regarding their wishes will be ignored and Aunt's estate will be distributed to her heirs (parents, if alive, then siblings if alive, then neices/nephews if no parents or surviving siblings), and your Uncle's estate will be distributed in a similar fashion. (assuming neither of them 120 hours longer than the other - if one did, then only the family of the later to pass will inherit.)
Unfortunately, more than 60% of Americans pass away without a will, often having expressed certain desires. It's necessary to take the extra step of having those desires written down and witnessed for them to be effective.
All of this being said, consult a probate attorney or probate litigator in your area.
One must assume the lawyer is ethical. Sadly, this is not always true. I suggest you consult and retain an attorney immediately. Everyone with knowledge should write memos. If no will is found, your other uncle and any sibling may have a superior claimthrough the Law of Intestate Succession. Your uncle will not look too wonderful if he was caught removing things from the house. If he is asking for Letters of Administration and not Letters Testamentary, he is probably saying there is no will. Does anyone remember him saying he wrote a will. You may want to challenge the issuance of the Letters of Administration if you can show your uncle may have committed misconduct. The Santa Clara County Public Guardian could be asked to serve. That way there would be a different lawyer as well (the County Counsel). This might fly better with the judge, but make sure you see a lawyer before going to the county.
In California, if no will is found it presumed destroyed. Your uncle would have then died intestate and the California Probate code would control the distribution of assets from the estate. The verbal remarks have no effect.
Any individual seeking legal advice for their own situation should retain their own legal counsel as this response provides information that is general in nature and not specific to any person's unique situation. Circular 230 Disclaimer - Advice given in this response cannot be used to eliminate penalties with the IRS or any other governmental agency.