What's to gain by lying about this?
Probably nothing, she just panicked finding a world famous actor dead and instead of calling the authorities sought reassurance about the situation. Unfortunately it now makes her look a little suspicious.
Agreed. I think the famous do themselves in in this regard. People don't take action because of fear if they overreact. The are probably trained to think of discretion. The people around them think of headlines and pause instead of act. In this case, it doesn't sound like her 'pause' made any difference. Sounds as though he was already dead and beyond rescuscitating.
Interestingly when the housekeeper came in a couple hours earlier I expect although he was sleeping(she said he was snoring), there were no pills about him(or I expect she would have picked them up or checked on him). Sounds as though he may have woken up anxious from that sleep and perhaps still groggy from its effects and not remembering what medication he last took or how much or even how much time had passed and overdosed. Maybe not even enough that he could not be revived, however somebody finding him took too long for them to do so. Just speculation from what's been said.