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When fitting models and doing anova, one uses the sum of squares.

But I've come across tools to do anova using only summary statistics (mean, sd or se, n) of groups to be compared.

Is this legitimate? Why or why not?

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You can certainly back out sums of squares from means, standard deviations and sample sizes, or from any summary that would let you figure out means, standard deviations and sample sizes.

A number of posts on site offer formulas for total variance given subgroup variances and means, for example; it's calculations like these that can be used to obtain the results you need to be able to do this.

If it's done correctly all the fitted values, sums of squares, residuals, tests etc are the same. In that sense it's just as legitimate as the version calculated from sums of squares of individual values.

However, one important problem is that you can't really assess the suitability of most of the assumptions you made in running your hypothesis tests, confidence intervals and so forth. For example, you have no residuals for doing any of the residual checking of suitable assumptions.

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