No they aren't. What I tried to get across was that the absence of interbreeding, whether or not it is possible, is a defining property of the working definition of speciation. The working definition does not perfectly reflect true speciation, but as the label implies, is a way to bridge communication gaps and as short hand.
There are many cases where two species can produce progeny but do not, either because there is a geological impediment to them, (allopatric speciation), as in the case of the Lion and Tiger, or because the two species just do not interbreed in nature (sympatric speciation) even though they share a geographic range. Of course we can change that because we are masters at manipulating other organisms.
In the case of the Greenish Warblers (Phylloscopus trochiloides), P. t. viridanus and P. t. plumbeitarsus do not interbreed, even though they are quite capable of doing so, because they do not recognize each other's songs and consequently do not identify each other as members of an interbreeding group.
Lions and tigers (and their crossbreed offspring) have fertlity levels well below what would be replacement levels in the wild. They are indeed speciated; they just aren't completely infertile. They almost never encounter each other in the wild anymore (although they probably used to before humans restricted their ranges). It's unlikely they would breed with each other absent confinement together by humans. Male tigers are particularly loath to breed with female lions, apparently considering them butt-ugly.
Lions also have some cross-fertility with leopards. This (and the fossil record) shows that the radiation of the big cats is a relatively recent thing.
There's a range of cross-fertilities visible in nature. It's what evolution predicts. Speciation is not an all-at-once thing. It takes time and cross-fertility in isolated groups drops smoothly rather than vanishing all at once.
We see every degree of relatedness in nature. Humans, before the age of exploration, were on the way to speciating based upon their geographic dispersal. It never got that far and now it never will because we've been remelding for centuries now.