Actually, Kobe did say the reverse was true. He said Shaq wouldn't have won the rings without him, and he wouldn't have won the rings without Shaq, and neither would have won the rings without Fisher, Horry, etc.
However, you're right in that failing to give Shaq more than half the credit is wrong. The truth is, I don't think there's any big man, or really anybody, you could have substituted into those Lakers teams for Shaq and still won the titles - maybe Duncan, maybe Garnett. At the time, Shaq was one of the 2 or 3 best players in the league and couldn't be replaced because he was better than pretty much everybody else.
However, you could have subbed about 5-10 wing players (Pierce, Carter, McGrady, Allen, Hill, Iverson, maybe even Finley, Miller, Stackhouse) in for Kobe (and about 20 overall - add Duncan, Garnett, Kidd, Payton, Dirk, Webber, Malone, probably even Marbury and Nash) and still won the titles.
That Kobe has won only one MVP seems a bit low but makes sense since he's only been the best player on his TEAM for 5-6 years, and his team failed to top 50 wins in 3 of those seasons. That Shaq won only one MVP in his career is a crime. He was the dominant force in the league from 98 to 02, during which time his teams won 61, 31 (pace for 51), 67, 56 and 58 games. I guess, realistically, his injuries are really what cost him more hardware. But there's a reason he has 4 titles and 3 Finals MVPs and Kobe has 3 and 0.
And there's a reason the Lakers were 245-84 (.744, equivalent of 61-21) with Shaq in the lineup from 98 to 02, but 28-21 (.571, equivalent of 47-35) without him. With Kobe in the lineup, they were 245-98 (.714, equivalent of 59-23) but 28-7 (.800, equivalent of 66-16) without him. Shaq was better, and more important, than Kobe.