How can a non-imported method in a not-attached package be found by calls to functions not having it in their namespace?

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I’m not sure if I correctly understand your question, but the main point is that group is character vector while data$group is factor.

After attaching gmodels, the call for reorder(factor) calls gdata:::reorder.factor.
so, reorder(factor(group)) calls it.

In transform, the function is evaluated within the environment of the first argument, so in T2 <- transform(data, group = reorder(group,-num)), group is factor.

UPDATED

library attaches the import packages into loaded namespace.

> loadedNamespaces()
 [1] "RCurl"     "base"      "datasets"  "devtools"  "grDevices" "graphics"  "methods"  
 [8] "stats"     "tools"     "utils"    
> library(gmodels) # here, namespace:gdata is loaded
> loadedNamespaces()
 [1] "MASS"      "RCurl"     "base"      "datasets"  "devtools"  "gdata"     "gmodels"  
 [8] "grDevices" "graphics"  "gtools"    "methods"   "stats"     "tools"     "utils"

Just in case, the reorder generic exists in namespace:stats:

> r <- ls(.__S3MethodsTable__., envir = asNamespace("stats"))
> r[grep("reorder", r)]
[1] "reorder"            "reorder.default"    "reorder.dendrogram"

And for more details

The call of reorder will search the S3generics in two envs:

see ?UseMethod

first in the environment in which the generic function is called, and then in the registration data base for the environment in which the generic is defined (typically a namespace).

then, loadNamespace registers the S3 functions to the namespace.

So , in your case, library(gmodels) -> loadNamespace(gdata) -> registerS3Methods(gdata).

After this, you can find it by:

> methods(reorder)
[1] reorder.default*    reorder.dendrogram* reorder.factor*    

   Non-visible functions are asterisked

However, as the reorder.factor is not attached on your search path, you cannot access it directly:

> reorder.factor
Error: object 'reorder.factor' not found

Probably this is whole scenario.

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