Yes. When you're working in the newsroom, you generally need to steer clear of accepting any gifts, free services, or free products. It really matters when it's from a company that the Times has covered, or might write about in the future -- but that's a pretty wide net, and most startup employees would arguably fall into that category. The Khan Academy's sponsored donation program certainly would.

Here's the actual language:

    Staff members may not accept gifts, tickets, discounts, 
    reimbursements or other inducements from any individuals 
    or organizations covered by The Times or likely to be 
    covered by The Times. (Exceptions may be made for trinkets 
    of nominal value, say, $25 or less, such as a mug or a cap 
    with a company logo.) Gifts should be returned with a polite 
    explanation.

From this little gem of a handbook: http://nytco.com/pdf/NYT_Ethical_Journalism_0904.pdf

... it's the Times' internal ethics rulebook specifically aiming at the conundrums of journalism -- but I think that quite a lot of it applies to ethical business practices in general.