Absolutely! Proofs are needed to make science advance, but when proofs are here, anything can be re-evaluated.
You have also the contrary case when people (sometimes even scientists - everyone is fallible) are looking so hard to find proof of the existence of a possibly extinct species that they completely exit the path of the scientific method, and it end up in fiascos (eg. the ivory bill woodpecker). It does not even mean it's for sure extinct (it is still an open question), but some of these papers that were written on the subject are... debatable.
They are also a huge amount of species that we know are not entirely extinct, only because scientists (and other professionals and amateurs) are keeping a close eye on them, sometimes since 100+ years.
But that's one of the times when one can feel a lot of resources could be spent to research possible surviving populations, because if it's the case, protection measures can be taken, and the species possibly saved. It's a big deal, and it's understandable to spend resources. However, many many cases like that exist, and a selection has to be done. They are many things to take in account to decide whether a study will be undertaken. I've never personally worked on possibly extinct whole species, but extinct/ going to extinction populations is something I'm very familiar with, especially the population genetics aspect of it (unfortunately, when a population - or worse, a species - is going extinct, it's often doomed much before the last specimen is dead, because you need a minimum genetic diversity in a population/species to be long term viable. For some species, that requires a rather large group, and it's extremely depressing to see a small but not minuscule population with healthy individuals going around doing their thing, but you already know the end is coming for the whole population
Not always fun, but fascinating stuff!