It's a very exciting thought, at least it would be - if it was true.
The last time that Birkat hachama fell on Erev Pessach was 5685 (1925) - there are people alive who still remember that event.
Historically Birkat has fallen on Erev Pessach several times, including the following years:
- 4369 (609)
- 4453 (693)
- 5069 (1309)
- 5685 (1925)
- 5769 (2009)
So although not common, Birkat HaChama has fallen on Erev Pessach far more than 3 times.
What's more, Yetziat Metzrayim is normally calculated as having been in 2448, however there was no Birkat Hachama that year, Birkat Hachama would have been 2437 and then again in 2465.
Similarly Purim was in 3405, hover the nearest Birkot Hachama would have been 3389 and 3417.
The Rabbis that I heard on the Radio are clearly basing their comments on the Kadosh Elyon who brings down the concept that Birkat Hachama will only occur three times in history on Erev Pessach, and the final time will be before the Redemption. I don't understand the message that the Kadosh Elyon was trying to portray, but it is clearly not a history or astrology lesson, as his claims don't make sense in a historic framework.
Why these Rabbis would repeat this claim on the radio as if it were historically accurate is beyond me, but maybe they have a deeper message that I missed.