Is it safe to download Flash directly from Adobe site?

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http://www.linuxforums.org – When I use the BBC site, I see messages "Cannot play media.You do not have the correct version of the flash player. Download the correct version" However, when I go to Applications > Ubuntu Software Centre, I get the message, "Adobe Flash Player is installed on this computer. It is used by 1 piece of installed software" I would be grateful for any advice. BTW: If I try to use the Firefox Adobe add-ins feature, I'm directed to the Adobe page. Is it safe to use this feature rather than, for example, Synaptic Package Manager? (HowTos)