A key function of scientific publication is to inform other researchers in the field about potentially interesting things as quickly as resonable. Getting "two more confirmations from separate teams" is a very high bar, as it's not about just asking a source, it's asking someone else to do all the same work again. Not only we don't require it before publication, we don't expect it to happen for the vast majority of publications ever. Important studies get replicated, but most don't get repeated ever. A partial explanation of the original article's observation is the (very many!) papers that don't have much citations and don't fail to replicate because nobody cared enough to put the work in to try.
If publication would require two more confirmations from separate teams, that would mean (a) doing the work in triplicate, so you get three times less results for the same effort; (b) the process would take twice as long as I spend a year doing the experiment and then someone else can start and spend a year doing the same experiment, and only then it gets published; (c) there's a funding issue - I have somehow got funding to spend many months of multiple people on this, but who's paying the other independent teams to do that?; (d) it's not a given that there are two other teams capable of doing the exact same research, e.g. if you want to publish a study on the results of an innovative surgery procedure, it's plausible that there aren't (yet!) any other surgeons worldwide who are ready to perform that operation, that will come some time after the publication; (e) many types of science really can't get a separate confirmation - for example, we have only one Large Hadron Collider, you can't re-do archeological digs, event-specific on-site sociological data gathering can't really be repeated, etc; so you have to take the data at face value.
What you describe is absolutely right, it is important to have this kind of communication. If publications were only the means to communicate, that would serve the purpose and won't be a problem. The problem is that they are considered having a second purpose - to create scientific reputation, based on which society allocates funds and prioritizes the research. The original article illustrates how wrong this approach can be, substituting the ability to produce scientific facts with the good story telling.
If publication would require two more confirmations from separate teams, that would mean (a) doing the work in triplicate, so you get three times less results for the same effort; (b) the process would take twice as long as I spend a year doing the experiment and then someone else can start and spend a year doing the same experiment, and only then it gets published; (c) there's a funding issue - I have somehow got funding to spend many months of multiple people on this, but who's paying the other independent teams to do that?; (d) it's not a given that there are two other teams capable of doing the exact same research, e.g. if you want to publish a study on the results of an innovative surgery procedure, it's plausible that there aren't (yet!) any other surgeons worldwide who are ready to perform that operation, that will come some time after the publication; (e) many types of science really can't get a separate confirmation - for example, we have only one Large Hadron Collider, you can't re-do archeological digs, event-specific on-site sociological data gathering can't really be repeated, etc; so you have to take the data at face value.