That's the argument of economic firm Bates White in a report that they released last September, on the grounds that the medical criteria in the FAIR Act are so permissive as to allow millions of non-asbestos-related claims on the fund. A Senate hearing on the 17th featured debate on the report.
The Asbestos Alliance supports the bill; the Coalition for Asbestos Reform opposes it as insufficient, while the trial lawyers' associations are concerned that the bill may limit the lawyers' take to seven billion or so dollars. "The ABA supports enacting federal legislation that would require claimants to meet specific medical criteria before filing action in non-malignant asbestos cases and would toll all applicable statutes of limitations until such time as the criteria are met."
Senators Jeff Sessions, John Cornyn, Charles E. Grassley, Jon Kyl, Lindsey O. Graham, Sam Brownback, and Tom Coburn have expressed reservations about the current version of the Specter-Leahy bill; their additional views in the Senate report (at pp. 91 ff. in the full pdf version) is must-reading on the subject. One problem with S. 852 is that it would override reforms in states that are fixing their asbestos litigation abuses, like Texas; Governor Rick Perry wrote President Bush in May to oppose the bill for this reason.
AEI's Kevin Hassett and Peter Wallison and economist Robert Shapiro are co-authors of a study "Assessing the Economic Impact of Proposed Asbestos Legislation" that suggests the benefits of the trust-fund approach are illusory.
An interesting alternative to the Specter-Leahy bill that hasn't gotten enough discussion is Rep. Chris Cannon's H.R. 1957, which has sixty co-sponsors, and provides meaningful reform of asbestos litigation through establishing medical criteria and limiting deep-pocket searches through a requirement of proportionate liability.