Where did you get this statement from? 4 seats abreast in transverse seating takes up the portion of the train car exactly equal to seat pitch i.e. the distance between rows. 4 seats longitudinally takes up the length exactly equal to the width of two seats. Width of two seats is generally greater than seat pitch, so longitudinal seating takes up more room, therefore fits fewer seats.
When you have transverse seating, decision makers have to pick a seat pitch aka the distance between a transverse seat and the one in front of it. They have to pick a distance based on average/median heights and femur lengths so it works for most people. Thus, there is always space between rows of transverse seats that cannot be used for standing whether the seats are occupied or not. There is effectively more floor space taken up by two rows of 2+2 transverse seats than two perimeter longitudinal benches seating 4 people each.
My assumption is that a hypothetical 4 person wide longitudinal bench ITSELF takes up the
exact same floor area as a 4 person wide transverse bench, which would also be the same floor area as 2+2 transverse benches with a middle aisle. They all take up the exact same surface area of the train car floor from a top down view like this.
In practice though, I think a single transverse seat will take up more space than a single longitudinal seat,
even though the seat itself takes up the same space as a longitudinal one. Imagine a case where a particularly short person occupies a transverse seat in a transverse only layout. They leave a huge gap in front of them to the seat in front of them. There would be no reasonable way for that space to be used even during peak afternoon rush hour. It would be highly awkward for a standing patron to insert themselves into that gap. There is always some legroom unused in transverse seating, unless all the seated patrons are giants.
There is no wasted provisioning for legroom in perimeter longitudinal seating. And psychologically, it's less of an invasion of personal space to have to share some legroom with a standing patron when you are seated longitudinally during a rush hour crush load. So I am taking into account soft real world factors.
If you are ok with taking up more floor space than a maxed out longitudinal only layout, then
transverse layouts can definitely offer more seats. But that wouldn't be ceteris paribus anymore. You are effectively occupying more floor space in order to get more seats; that is not all other factors being the same. See my reply to
@KhalilHeron above.
My ultimate point was to reiterate that transverse, given the same floor area occupied by seating, will offer less seats because seat pitch has to be taken into account, which is never optimal for each individual; this also comparatively reduces usable standing space. Longitudinal seating technically has virtually* unlimited leg room, only constrained by crush loads rarely seen in Toronto. (edit*)
That is all not to mention that longitudinal flat bench seats make it more appealing for patrons to sit closer together shoulder to shoulder. Again in cases of smaller patrons, you would be hard pressed to have 3 of them share the seating area designed for 2 average-sized patrons in transverse seating. Conversely, 3 smaller patrons sharing the seat area designed for 2 average patrons on a longitudinal bench would be entirely feasible.
