False.
I don't know what would constitute 'reliable' in your mind, given the usual position taken by Muslims that any site remotely critical of Islam is a biased site incapable of being correct on even the smallest factual detail and, if not that, then the site caters to a different sect to the one of which the person speaking happens to be a member, and is therefore, naturally, bulls--t.
Anyway,
this site usually seems to be well-received by the Sunni members, so let's hope I don't get mauled for my 'Islamophobic' ignorance.
Cutting out the silly apologetics ('Europe and America were worse in their time!'
, the most salient point is as follows:
You're welcome to read the rest of that exercise in excuse-making, but since you've only disputed the permissibility of slavery in Islam, much of it is irrelevant (it goes into quite some detail about why slavery in Islam is justified/ameliorated because, hey, Judaism and Christianity were just as bad if not worse).