"Lofty claims" refers to statements or assertions that are bold, grandiose, or exaggerated. It implies that someone is making confident declarations that may be overly ambitious or not easily supported or proven. Full definition
However, there are various online custom service providers that would make lofty claims but fail to provide the best and the expected results. (professaywriters.com)
Those are fairly lofty claims (health care costs don't really come down in tandem with improving care quality). (fortune.com)
It seems to be a pretty lofty claim, but I can not seem to find any scientific information to support it. (nutritionfacts.org)