I'm going to try and address a number of points that have been discussed.
To summarize, There is no definitive evidence that the Daleks are legally required to appear in every season. This implies that there is also no evidence to definitively DISprove the rumor, as well.
In England (and many other countries) the person who creates a character for a show owns the character, and retains rights to same. the "Work for Hire" model is somewhat unique to America. This is why there is always a credit for the creators of any monster or character - Kit Pedler and Gerry Davis for the Cybermen, Bob Baker and Dave Martin for K-9, etc.
The Daleks have been owned by Terry Nation (and now his estate) since their creation in 1963. There was a brief period diring the original series that they did not appear because he was attempting to shop them to America for a series. That never panned out, so they returned after a couple year sabbatical.
The BBC has never owned the rights to the Daleks, but not everybody at the BBC knew that. The Daleks almost didn’t make it to the new series of Doctor Who, and it was all Steve Martin’s fault. When he was to appear in the film Looney Tunes: Back in Action, he insisted they include a Dalek in a madcap scene full of old movie aliens. He was a big fan of the series, and thought it’d be a nice tip of the hat. Permission was asked of the BBC, but not of the estate of Terry Nation, who controls the rights to the characters. This caused offense, so when the BBC asked to bring them back for the new series, the estate originally refused. When Steve Martin heard about it, he wrote a personal letter to the estate explaining the situation, and apologizing profusely. This calmed everyone down, and the proper paperwork was signed to allow the characters to appear. But for about a month, writer Robert Sherman was forced to work on a draft of the script for "Dalek" with another alien.
It is not impossible for such a requirement to be included in a contract, however. Wonder Woman is the best example. For decades, DC Comics did not actually own the rights to Wonder Woman, they licensed her from the William Marston estate. One of the clauses in the contract was that they had to continue to publish a monthly Wonder Woman comic, This was because for many years, while the book did not sell well, Wonder Woman merchandise was very profitable. The estate didn't want DC to get the rights and never do a comic, just making money off the toys and t-shirts.
As of right now, new showrunner Chris Chibnall has said that NO old monsters or aliens would appear in Jodie Whittaker's first season, Daleks included. Now, it's very possible that this is a clever lie - the specific answer in the interview was "We've got two weeks left to shoot and we haven't see any[Daleks] yet!" so they could be saving them for the veryveryvery end to try to keep things mum.
Moffat's comments, mentioned elsewhere, go on to say that people love the Daleks, and as a kid he wanted them to appear constantly. That seems to be the most logical reason they've appeared so often, but giving them a break would be a good idea in many people's opinion.