Well, no. See in order to include both grizzlys and koalas in the same clade, that would pretty much mean every mammal on earth would be a “bear”. Whitetail Deer would become whitetail bears.
However, actually the scientific community doesnt use the term "bear’ really, they use binomial nomenclature, which is in latin.
There’s no reason that the ordinary English word “bear” must indicate a clade. It just indicates any creature that is popularly known as a bear.
Then why do we see people making statements like “a chump is not a monkey” and “a koala is not a bear”? If the word “bear” is not actual scientific nomenclature then scientists ought to stop trying to correct its usage.
A chump may not be a monkey, but most monkeys are chumps. 
Just look what they are willing to do for bananas.
By current thinking, Chimpanzees are monkeys, if “monkey” is to have any scientific/cladistic meaning. Chimps are apes, old world monkeys are more closely related to apes than they are to new world monkeys, so either new world monkeys aren’t monkeys, or apes are a particular kind of monkey.
What’s a virius?
A member of the taxon of organisms with incorrect Latinate plurals. Very exclusive group.
Singular for cattle is “beef critter”, viz. numerous episodes of The Beverly Hillbillies.
But are the people who make these statements genuine scientists, or are they, in fact, common-or-garden variety smart-arses (pedantica domesticus)?
I find you can often spot the former by their distinctive cry of “Actually…”