The Big Lie
Organisers of the Swiss Indoors and some other people try to justify sponsorship of the Basel tournament by denying or minimizing its link to tobacco, claiming instead that Davidoff sells "fragrances and other accessories" and describing it as a "luxury good provider". This is simply a Big Lie.
In terms of revenues, Davidoff is first and foremost a tobacco brand. Luxury items, however, are also sold under the Davidoff name. This is the result of an elaborate brand stretching strategy.
Indeed, according to an internal BAT document, the non-tobacco Davidoff products provide "alibi advertising opportunities" for the cigarette brand, especially in countries with tobacco marketing restrictions (see Davidoff brand stretching).
But the two brands, although they use the same name, can hardly be confused: since 2005, they have different logos. And it is the Davidoff tobacco logo that appears in the Centre Court in Basel and decorates the uniforms of the tournament staff.
It is not arguable that the Basel tournament is sponsored by the tobacco branch of the Davidoff group. The sponsor makes no secret that his business is tobacco. On the website of the Davidoff Swiss Indoors, the page dedicated to the welcome word from the title sponsor shows Reto Cina, the chairman of all the tobacco companies of the Oettinger Davidoff group, smoking a cigar in a tobacco shop. His welcome text is simply a variation on the theme "Davidoff The Good Life", which is a registered trademark of tobacco company Davidoff & Cie SA in Geneva.
The presentation of the title sponsor on the tournament website is even more blatant. This is nothing but a marketing pitch for the "Davidoff The Good Life" brand name.
Davideath - The Ugly Death
The UK Intellectual Property Office classifies goods into 45 classes. Class 34 is exclusively dedicated to tobacco products. Among the 94 registered trademarks which contain the word "Davidoff", 62 are in non-tobacco classes, with individual trademarks often covering several non-tobacco classes, while the remaining 32 trademark are uniquely in the tobacco class. Furthermore, the non-tobacco trademarks have all as proprietor Zino Davidoff SA in Fribourg (Switzerland), while the tobacco trademarks have as their proprietor Davidoff & Cie SA in Geneva. The two types of trademark, tobacco and non-tobacco, are very clearly separated. Things are well done: the Davidoff trademark diversification scheme is neatly elaborated.
The UK Intellectual Property Office lists two entries for "Davidoff The Good Life" (M692896 and U00000692896), both of which belong to class 34, tobacco goods.
Finally, the link indicated on the title sponsor page shown above, www.davidoff.com, points to website of Davidoff & Cie SA, the tobacco company of the Davidoff group, which handles the tobacco Davidoff trademark on behalf of Imperial Tobacco. 
It is interesting to note that, when clicking on such link, you get different messages depending on the country where you are.
In Switzerland and France, for example, you get a screen containing nothing but the minimalist welcome message shown on the right. When you click on "Welcome to Davidoff", you are subjected to the age check below, in the same illusory vein as the protection used for porno sites!
In the UK, accessing www.davidoff.com gives an entirely different result. You get a screen displaying the following message:
"We are sorry but due to UK legislation we are not allowed anymore to show you our website www.davidoff.com. Thank you for your understanding." and you are blocked from proceeding any further.
Given all what precedes, a sponsor who, for his presentation, uses "Davidoff The Good Life" and the www.davidoff.com website, leaves no place for doubt that he is in the tobacco business. Saying and repeating the contrary in the face of evidence is nothing but resorting to the infamous Big Lie propaganda technique.