No, it is not a valid objection. In discovery, the opposing party has a right to see (and have copies of) every copy of a particular document.
For example, let's say the plaintiff wrote the defendant a letter. The plaintiff has the letter, but maybe the defendant wrote notes on the copy the defendant received. Maybe the defendant made multiple copies and gave it to various employees, who all made notes on it. The plaintiff is entitled to production of all unique copies. Plus securing a copy from the defendant assures that the plaintiff knows exactly what the defendant believes the copy was--it avoids (or timely raises) the issue of modification of the document.
This response is provided as general information only. It is not intended to be legal advice. Legal advice must be based on the exact facts of the particular situation, and by necessity this forum is not appropriate for discussion of specific, exact facts. Contact a lawyer for more specific advice. My answer to your question on AVVO does not create an attorney-client relationship.
No, this is not a proper objection/response under Code of Civil Procedure section 2031.210.
The information presented here is general in nature and is not intended, nor should be construed, as legal advice. This posting does not create any attorney-client relationship with the author (who is only admitted to practice law in the State of California). For specific advice about your particular situation, consult your own attorney.
The short answer is no. You always have a right to ask the other party what documents they have. This may (or may not) match up with what you think they should have.
Perhaps they do not have a document you mailed them. This is often something that is important to know.
Perhaps they have a document in their file that you don't have. Perhaps you mailed them a letter and failed to keep a copy of it. This is ALWAYS important to know.
I am admitted to practice in Connecticut and limit my responses to CT law.
For the purposes of this response, I am going to assume that by "producing party" you are referring to a party in a civil case (Plaintiff or Defendant) who is responding to a discovery request, and not someone who is responding to a subpoena.
In a civil case, it is very common for a responding (Producing) party to object to the request because the documents "are already in the possesion of the requesting party, or readily available to the requesting party." Sometimes this objection is made where a party requests documents that they should be able to obtain without propounding discovery; one example is if you request copies of emails which you should have in your email account. Despite the objection that the documents are already in your possession, however, the responding party should produce the documents unless it is truly burdensome for them to do so (too many hours to search for them, thousands of pages, etc.) You could send a meet and confer letter and request that the documents be produced and then file a motion to compel the production.
Also, you said that it is not a valid objection that the documents are available from a public entity; that is not true. Depending on the documents sought, one could object that the documents are "readily available" from public entities or on public resources (such as the internet or count recorder/clerk's office).