It Has (Almost) Always Been Floor
Since at least 1968, with Dartmouth BASIC V4, the behaviour of INT is defined as as delivering an integer not greater as X - which otherwise may be called FLOOR. This is consistent with all BASIC I know.
Why? Because Enhanced Usability
Truncate can only be used to relief float numbers from their fractions. To use it for rounding sign handling needs to be implemented different for positive and negative numbers, requiring a 4 line construct:
100 If I < 0 THEN 130 110 I = INT(I+0.5) 120 GOTO 140 130 I = INT(I-0,5) 140 ... In contrast a Floor implementation works independent of the sign always in the same 'direction', enabling easy use in single statement of
I = INT(I+0.5)
Same would have been true for use of Ceiling(*1), except Floor also works like Truncate for all positive numbers. Something easy to understand for beginners (students) thus a perfect compromise for a teaching language. One function good to show two very common use cases.
Some Archaeology
A good starting point in search for default behaviour of BASIC are always the ECMA standards 55 for Minimal BASIC (1978) and 110 for 'full' BASIC (1985). For an item as basic as INT ECMA-55 notes:
(ECMA-55 section 9.4 on page 12)
European ECMA-55 standard which is essentially the same as US ANSI X3.60-1978 standard, which in turn is based on SBASIC, an intermediate step between Dartmouth V6 and V7 made in 1976. Since it was implemented as preprocessor for V6 it can be assumed that Dartmouth BASIC V6 created in 1969, published in 1971 as well used INT with the same definition.
Looking into the 1968 V4 documentation shows the same behaviour
(Page 42 of the BASIC Version 4 manual)
Going back to V2 of 1964 shows different:
(Page 39 of the BASIC Version 2 manual)
This quite complex explanation already shows why Truncate isn't as great for a beginners language as Floor.
The change from 'Floor' to 'Truncate must have happened before V4 and considerable before it gathered wide spread use. This also shows why all later BASIC employ the same workings. No matter if 1975 Prime BASIC or 1991 Visual BASIC.
*1 - At that point it may become obvious that the function group to look at isn't the mentioned tripple of Truncate/Floor/Ceiling but a quadruple including ROUNDING as well.