Employment contracts also carry non-compete clauses which can prevent you from (a) making anything that can complete with the company in its current or anticipated line of business [1], (b) have policies for outside employment that may restrict all but employments that are completely unrelated to the company (like running a family-owned shop, etc.), and (c) disallow even make plans to form a business entity that the company may consider to be potentially competing with their current or anticipated line of business.
The above is largely coming from my contract from a previous employer. I have seen contracts of at least two other big-name companies and they were similarly restrictive.
[1] AFAIK, the legal definition of "line of business" is quite broad. It was suggested that something falling within the same trademark code would be considered to be the same line of business. Computers and software fall under a single class [2]. So an enterprise content-management system and an iPhone game both would fall under the same line of business.
My bet is that they are doing it in spite of their employment contracts, as opposed to the contracts allowing them to do those projects. Let me know in case you check with them. This usually works out because most (statistically) will never make enough money to be a target of a lawsuit.
I am currently full time on my projects, so do not have such legal issues anymore. When I did, I had started looking around to find out which companies have better contracts and who all people do not have such issues. It was largely an empty set. One big-name company had the contract optional with the condition that if you do not sign it when joining, you do not get bonus/stocks in the company during performance reviews (only the base salary and benefits).
I had also posed these questions to several wannabe founders as well as a few successful ones at YC Startup School and elsewhere. Nearly all people in the first category had never read their contracts ever, while the people in the second category became tight-lipped right away and diverted the question. One from the latter category told me that incoming lawsuits are commonplace for his company but that I should not worry about them because lawsuits come only after the company also gets some money to deal with them.
Legally you can change any and all parts of a contract (more or less, law superceeds contracts obv.). It's all just a matter of finding a mechanism or method to edit the contract.
You are not suggesting, are you, that they cannot refuse to accept the changes to the contract, which by itself is said to be a condition for the employment?
Sure they can refuse any changes. And you can refuse any changes. But then you don't have a contract, and then you don't have an employement.
So if they say "We'll give you a job, under conditions X, Y, Z" and you say "I don't like Y", they could either say (a) "Well, OK, we'll offer you a job under conditions X and Z" (in which case you have a job), or (b) "Sorry Y is a deal breaker for us, no deal" in which case you don't have a job.
