Sorry but that simply isn't true. Nairobi has got a lot of things going for it, but safety isn't one of them. I've spent six months in Kenya and still have the scars of a machete attack that three guys were kind enough to carry out on me. Though the level of violence in my case was worse than in many other examples, it was not an isolated case - whilst I was there several other people I met were mugged in Nairobi, one very unfortunate guy twice in one day! Lonely Planet is quite right to warn of the potential dangers in Nairobi and along the coastlines to the north and south of Mombassa. Attacks are not confined to 'dark alleys' nor to nighttime (though these are obviously better avoided) - mugging can occur in crowded strreets and during the day.
This said, birding in Kenya is fantastic and no one should be put off ...just don't go wandering with binoculars or other valuables in Nairobi city or, without local knowledge (eg from your hotel), the areas along the coast. In fact, by and large, just skip Nairobi (except perhaps Nairobi National Park) - it is not a particularly attractive place and birding is a billion times better elsewhere in the country.