A base ticket is one major (theme) park per day. You are allowed to re-enter the same park if you leave it on one day, but it can only be used at the one park.
Note that the ticket will state on it either "Not Valid For Park Hopping" or "One Theme Park Per Day". That should be a hint.
If you put the ticket in the turnstile of another park the display on the Guest side of the turnstile will be "ACCESS DENIED". The top line of the display on the Greeter side will give information about the ticket, and the second line of the display will say "CROSSOVER NOT PERMITTED". The turnstile will not unlock.
This is because Disney charges $3.00 per day over four days on a ticket, but charges $52 to allow hopping. It does not make economic sense for Disney to allow this.
If you actually have multiple tickets (more than one physical ticket per person) as opposed to multiple day tickets, you can use these tickets for multiple entries. But it makes absolutely no economic sense as a separate ticket costs a lot more than adding hopping to a ticket.
Or, as I recently told a Guest who was arguing with me about using a different day on the ticket:
The turnstile computer thinks today is Friday. The turnstile computer at the other park also thinks today is Friday. The two turnstile computers talk to each other. If you can convince this turnstile computer that today is not the same Friday as the other computer thinks, it will let you in.
When you call Walt Disney World, unless you really know a direct number, you will get one of two offices.
The Disney Reservations Center (DRC) includes Walt Disney Travel Company (WDTC), Central Reservations Office (CRO), Disney Dining, and some other lesser known information lines. To the best of my knowledge the DRC locations are in the International Drive area, Tampa, Houston, Salt Lake City and somewhere in North Carolina. There may be more. Some of the people working at the DRC call centers may never have been to either WDW or DL (or both).
The Main Switchboard (407-824-2222) is also where all calls to Disney Resorts go if you are dialing the phone number on the back of your reservations form. Also that is where calls go if you dial the Operator from your room, and possibly even calls to the Front Desk. The Main Switchboard people will, if asked, also identify themselves as Guest Services. They can put you through to any number on WDW.
At both DRC and MS they have access to a computer which has lots of Guest Information and it is very well organized. Actually, all CMs who have access to a terminal, or who even can access the "Cast Portal" from off-site, have access to this Guest Services information. I will often open an extra window when I am responding to people and go into the Portal for the latest official information.
The people at DRC and MS do not deal with upgrades, partially used tickets, or problems related to tickets. They do not know all the rules. The people at DRC can sell unused tickets; the people at MS don't deal with tickets at all.
The people who work in the ticket booths at the Parks or in Guest Relations at the Parks (and this includes TTC, the Water Parks, and GRO in DTD) deal with ticket upgrades and unusual problems on a daily basis. I would not say that someone you talked to on the phone lied to you, but just they were attempting to answer a question when they really did not have an answer.