0000-01-01 is a valid date: January 1 0000, while 0000-00-00 is not (neither zero month, nor zero day are in calendar).

But I'm not expecting a valid value for the date since the value to be used is going to be the time; I was expecting that only the data to be used (the time at this case) was set.

https://godoc.org/time#Parse

Elements omitted from the value are assumed to be zero or, when zero is impossible, one, so parsing "3:04pm" returns the time corresponding to Jan 1, year 0, 15:04:00 UTC (note that because the year is 0, this time is before the zero Time). Years must be in the range 0000..9999. The day of the week is checked for syntax but it is otherwise ignored. 

time.Parse returns a time.Time object, which represents a moment in time. There is no split between date and time, so it can't return the one and not the other. 0000-00-00 does not exist so there is no way to represent it as a time.Time.

This is working as expected and as documented (#29902 (comment)).

But since the zero value (at date) of time.Time{} is set to "0001-01-01", then I think that such value also should be used instead of (0000-01-01).

https://play.golang.org/p/i2hFFIVQvbP

I don't necessarily disagree, but since this behavior is documented it falls under the Go 1 Compatibility Promise and can't be changed.

Elements omitted from the value are assumed to be zero or, when zero is impossible, one, so parsing "3:04pm" returns the time corresponding to Jan 1, year 0, 15:04:00 UTC (note that because the year is 0, this time is before the zero Time). Years must be in the range 0000..9999. The day of the week is checked for syntax but it is otherwise ignored.

Added a proposal for Go 2: #30086