If that happens in MySQL then it's a quirk to MySQL. Since you asked about other databases as well I decided to test it out on my postgres database. On a table with a little over 70 million rows it produces exactly the same explain for the following two queries (with the index):

explain select * from myschema.my_list where my_column in (232);
explain select * from myschema.my_list where my_column = 232;

which is:

'Bitmap Heap Scan on my_list  (cost=68093.11..4109456.90 rows=1656844 width=994)'
'  Recheck Cond: (my_column = 232)'
'  ->  Bitmap Index Scan on my_list_2  (cost=0.00..67678.90 rows=1656844 width=0)'
'        Index Cond: (my_column = 232)'

It doesn't diverge until I add in multiple elements in the list:

 explain select * from myschema.my_list where my_column in (232,79);
 explain select * from myschema.my_list where my_column = 232 or my_column = 79;

which is (respectively):

'Bitmap Heap Scan on my_list  (cost=172208.28..7050980.15 rows=4290987 width=994)'
'  Recheck Cond: (my_column = ANY ('{232,79}'::integer[]))'
'  ->  Bitmap Index Scan on my_list_2  (cost=0.00..171135.53 rows=4290987 width=0)'

' Index Cond: (my_column = ANY ('{232,79}'::integer[]))'

'Bitmap Heap Scan on my_list  (cost=177390.73..7066890.07 rows=4230402 width=994)'
'  Recheck Cond: ((my_column = 232) OR (my_column = 79))'
'  ->  BitmapOr  (cost=177390.73..177390.73 rows=4290987 width=0)'
'        ->  Bitmap Index Scan on my_list_2  (cost=0.00..67678.90 rows=1656844 width=0)'
'              Index Cond: (my_column = 232)'
'        ->  Bitmap Index Scan on my_list_2  (cost=0.00..107596.63 rows=2634142 width=0)'
'              Index Cond: (my_column = 79)'

I would take his answer with a grain of salt.

If that happens in MySQL then it's a quirk to MySQL. Since you asked about other databases as well I decided to test it out on my postgres database. On a table with a little over 70 million rows it produces exactly the same explain for the following two queries (with the index):

explain select * from myschema.my_list where my_column in (232);
explain select * from myschema.my_list where my_column = 232;

which is:

'Bitmap Heap Scan on my_list  (cost=68093.11..4109456.90 rows=1656844 width=994)'
'  Recheck Cond: (my_column = 232)'
'  ->  Bitmap Index Scan on my_list_2  (cost=0.00..67678.90 rows=1656844 width=0)'
'        Index Cond: (my_column = 232)'

It doesn't diverge until I add in multiple elements in the list:

 explain select * from myschema.my_list where my_column in (232,79);
 explain select * from myschema.my_list where my_column = 232 or my_column = 79;

which is (respectively):

'Bitmap Heap Scan on my_list  (cost=172208.28..7050980.15 rows=4290987 width=994)'
'  Recheck Cond: (my_column = ANY ('{232,79}'::integer[]))'
'  ->  Bitmap Index Scan on my_list_2  (cost=0.00..171135.53 rows=4290987 width=0)'
'        Index Cond: (my_column = ANY ('{232,79}'::integer[]))'

'Bitmap Heap Scan on my_list  (cost=177390.73..7066890.07 rows=4230402 width=994)'
'  Recheck Cond: ((my_column = 232) OR (my_column = 79))'
'  ->  BitmapOr  (cost=177390.73..177390.73 rows=4290987 width=0)'
'        ->  Bitmap Index Scan on my_list_2  (cost=0.00..67678.90 rows=1656844 width=0)'
'              Index Cond: (my_column = 232)'
'        ->  Bitmap Index Scan on my_list_2  (cost=0.00..107596.63 rows=2634142 width=0)'
'              Index Cond: (my_column = 79)'

I would take his answer with a grain of salt.