accuracy of GLM dispersion parameters

I'm confused as to the trustworthiness of the dispersion parameters
reported by glm. Any help or advice would be greatly appreciated.

Specifics: The summary function says that my fitted GLM has a dispersion
parameter=15.8. On the other hand, the gamma.dispersion function (MASS)
says that the GLM uses a dispersion parameter of 1.86. I could understand
some modest difference, as the help for gamma.shape() says that the MASS
functions return a more accurate dispersion value than summary(). However,
these two numbers differ by a factor of 8, which is quite a lot. Is this
normal? Would you folks expect such a large difference? Which value should
I trust?

R terminal excerpt:

summary(tempglm_g2)

Call:
glm(formula = precip_sbi ~ precip_oxx + precip_oxx_sq, family = Gamma(link
= identity),
    data = w.combo, start = c(0.1, 0.4, 0.02))

Deviance Residuals:
     Min        1Q    Median        3Q       Max
-2.99999  -1.63183  -1.00720   0.04878   8.93461

Coefficients:
              Estimate Std. Error t value Pr(>|t|)
(Intercept)    0.09236    0.04834   1.911   0.0583 .
precip_oxx     0.26848    0.35891   0.748   0.4558
precip_oxx_sq  0.05138    0.13418   0.383   0.7024
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

(Dispersion parameter for Gamma family taken to be 15.78978)

    Null deviance: 528.73  on 130  degrees of freedom
Residual deviance: 305.81  on 128  degrees of freedom
AIC: -100.33

Number of Fisher Scoring iterations: 5

library(MASS)
gamma.shape(tempglm_g2)

Alpha: 0.53807358
SE:    0.05526108

gamma.dispersion(tempglm_g2)

[1] 1.858482