You’re right that there are some complexities to this but that is no reason to abandon a perfectly good and fairly common sense tool we can use to categorize creatures.
A good rule of thumb is that if two types of animals can breed (or if they can both independently breed with another species as you noted), that is positive evidence of a common ancestry, but the inability to breed can never in and of itself be positive evidence of a lack of common ancestry.
At least in a strictly evolutionary-descent model it is.
In a progressive creation model, all bets are off.